<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2020 Workiva-->
<!--r:fe8fd34d-cbb2-44ca-bc3b-ac92660f95c2,g:9990f357-d41e-40c1-8eda-a039985fb06d-->
<xs:schema xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:swm="http://www.swmintl.com/20200930" xmlns:xbrli="http://www.xbrl.org/2003/instance" xmlns:nonnum="http://www.xbrl.org/dtr/type/non-numeric" xmlns:num="http://www.xbrl.org/dtr/type/numeric" xmlns:xbrldt="http://xbrl.org/2005/xbrldt" attributeFormDefault="unqualified" elementFormDefault="qualified" targetNamespace="http://www.swmintl.com/20200930">
  <xs:import namespace="http://fasb.org/srt/2020-01-31" schemaLocation="http://xbrl.fasb.org/srt/2020/elts/srt-2020-01-31.xsd"/>
  <xs:import namespace="http://fasb.org/us-gaap/2020-01-31" schemaLocation="http://xbrl.fasb.org/us-gaap/2020/elts/us-gaap-2020-01-31.xsd"/>
  <xs:import namespace="http://www.w3.org/1999/xlink" schemaLocation="http://www.xbrl.org/2003/xlink-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/instance" schemaLocation="http://www.xbrl.org/2003/xbrl-instance-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/2003/linkbase" schemaLocation="http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd"/>
  <xs:import namespace="http://www.xbrl.org/dtr/type/non-numeric" schemaLocation="http://www.xbrl.org/dtr/type/nonNumeric-2009-12-16.xsd"/>
  <xs:import namespace="http://www.xbrl.org/dtr/type/numeric" schemaLocation="http://www.xbrl.org/dtr/type/numeric-2009-12-16.xsd"/>
  <xs:import namespace="http://xbrl.org/2005/xbrldt" schemaLocation="http://www.xbrl.org/2005/xbrldt-2005.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/country/2020-01-31" schemaLocation="https://xbrl.sec.gov/country/2020/country-2020-01-31.xsd"/>
  <xs:import namespace="http://xbrl.sec.gov/dei/2019-01-31" schemaLocation="https://xbrl.sec.gov/dei/2019/dei-2019-01-31.xsd"/>
  <xs:annotation>
    <xs:appinfo>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="swm-20200930_cal.xml" xlink:role="http://www.xbrl.org/2003/role/calculationLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="swm-20200930_def.xml" xlink:role="http://www.xbrl.org/2003/role/definitionLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="swm-20200930_lab.xml" xlink:role="http://www.xbrl.org/2003/role/labelLinkbaseRef" xlink:type="simple"/>
      <link:linkbaseRef xmlns:xlink="http://www.w3.org/1999/xlink" xlink:arcrole="http://www.w3.org/1999/xlink/properties/linkbase" xlink:href="swm-20200930_pre.xml" xlink:role="http://www.xbrl.org/2003/role/presentationLinkbaseRef" xlink:type="simple"/>
      <link:roleType id="CoverPage" roleURI="http://www.swmintl.com/role/CoverPage">
        <link:definition>0001001 - Document - Cover Page</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CondensedConsolidatedStatementsofIncome" roleURI="http://www.swmintl.com/role/CondensedConsolidatedStatementsofIncome">
        <link:definition>1001002 - Statement - Condensed Consolidated Statements of Income</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CondensedConsolidatedStatementsofComprehensiveIncomeLoss" roleURI="http://www.swmintl.com/role/CondensedConsolidatedStatementsofComprehensiveIncomeLoss">
        <link:definition>1002003 - Statement - Condensed Consolidated Statements of Comprehensive Income (Loss)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CondensedConsolidatedBalanceSheets" roleURI="http://www.swmintl.com/role/CondensedConsolidatedBalanceSheets">
        <link:definition>1003004 - Statement - Condensed Consolidated Balance Sheets</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CondensedConsolidatedBalanceSheetsParenthetical" roleURI="http://www.swmintl.com/role/CondensedConsolidatedBalanceSheetsParenthetical">
        <link:definition>1004005 - Statement - Condensed Consolidated Balance Sheets (Parenthetical)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CondensedConsolidatedStatementsofChangesinStockholdersEquity" roleURI="http://www.swmintl.com/role/CondensedConsolidatedStatementsofChangesinStockholdersEquity">
        <link:definition>1005006 - Statement - Condensed Consolidated Statements of Changes in Stockholders' Equity</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CondensedConsolidatedStatementsofChangesinStockholdersEquityParenthetical" roleURI="http://www.swmintl.com/role/CondensedConsolidatedStatementsofChangesinStockholdersEquityParenthetical">
        <link:definition>1006007 - Statement - Condensed Consolidated Statements of Changes in Stockholders' Equity (Parenthetical)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CondensedConsolidatedStatementsofCashFlow" roleURI="http://www.swmintl.com/role/CondensedConsolidatedStatementsofCashFlow">
        <link:definition>1007008 - Statement - Condensed Consolidated Statements of Cash Flow</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="General" roleURI="http://www.swmintl.com/role/General">
        <link:definition>2101101 - Disclosure - General</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="GeneralPolicies" roleURI="http://www.swmintl.com/role/GeneralPolicies">
        <link:definition>2202201 - Disclosure - General (Policies)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="GeneralDetails" roleURI="http://www.swmintl.com/role/GeneralDetails">
        <link:definition>2403401 - Disclosure - General (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="RevenueRecognition" roleURI="http://www.swmintl.com/role/RevenueRecognition">
        <link:definition>2104102 - Disclosure - Revenue Recognition</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="RevenueRecognitionTables" roleURI="http://www.swmintl.com/role/RevenueRecognitionTables">
        <link:definition>2305301 - Disclosure - Revenue Recognition (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="RevenueRecognitionDetails" roleURI="http://www.swmintl.com/role/RevenueRecognitionDetails">
        <link:definition>2406402 - Disclosure - Revenue Recognition (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="OtherComprehensiveLoss" roleURI="http://www.swmintl.com/role/OtherComprehensiveLoss">
        <link:definition>2107103 - Disclosure - Other Comprehensive Loss</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="OtherComprehensiveLossTables" roleURI="http://www.swmintl.com/role/OtherComprehensiveLossTables">
        <link:definition>2308302 - Disclosure - Other Comprehensive Loss (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="OtherComprehensiveLossComponentsofAccumulatedComprehensiveIncomeDetails" roleURI="http://www.swmintl.com/role/OtherComprehensiveLossComponentsofAccumulatedComprehensiveIncomeDetails">
        <link:definition>2409403 - Disclosure - Other Comprehensive Loss - Components of Accumulated Comprehensive Income (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="OtherComprehensiveLossChangesinComponentsofOtherComprehensiveIncomeDetails" roleURI="http://www.swmintl.com/role/OtherComprehensiveLossChangesinComponentsofOtherComprehensiveIncomeDetails">
        <link:definition>2410404 - Disclosure - Other Comprehensive Loss - Changes in Components of Other Comprehensive Income (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="BusinessAcquisitions" roleURI="http://www.swmintl.com/role/BusinessAcquisitions">
        <link:definition>2111104 - Disclosure - Business Acquisitions</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="BusinessAcquisitionsTables" roleURI="http://www.swmintl.com/role/BusinessAcquisitionsTables">
        <link:definition>2312303 - Disclosure - Business Acquisitions (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="BusinessAcquisitionsDetails" roleURI="http://www.swmintl.com/role/BusinessAcquisitionsDetails">
        <link:definition>2413405 - Disclosure - Business Acquisitions (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="BusinessAcquisitionsScheduleofAssetsandLiabilitiesAcquiredDetails" roleURI="http://www.swmintl.com/role/BusinessAcquisitionsScheduleofAssetsandLiabilitiesAcquiredDetails">
        <link:definition>2414406 - Disclosure - Business Acquisitions - Schedule of Assets and Liabilities Acquired (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="BusinessAcquisitionsScheduleofIntangibleAssetsDetails" roleURI="http://www.swmintl.com/role/BusinessAcquisitionsScheduleofIntangibleAssetsDetails">
        <link:definition>2415407 - Disclosure - Business Acquisitions - Schedule of Intangible Assets (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="BusinessAcquisitionsScheduleofSalesandIncomefromBusinessCombinationDetails" roleURI="http://www.swmintl.com/role/BusinessAcquisitionsScheduleofSalesandIncomefromBusinessCombinationDetails">
        <link:definition>2416408 - Disclosure - Business Acquisitions - Schedule of Sales and Income from Business Combination (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="NetIncomePerShare" roleURI="http://www.swmintl.com/role/NetIncomePerShare">
        <link:definition>2117105 - Disclosure - Net Income Per Share</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="NetIncomePerShareTables" roleURI="http://www.swmintl.com/role/NetIncomePerShareTables">
        <link:definition>2318304 - Disclosure - Net Income Per Share (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="NetIncomePerShareDetails" roleURI="http://www.swmintl.com/role/NetIncomePerShareDetails">
        <link:definition>2419409 - Disclosure - Net Income Per Share (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="Inventories" roleURI="http://www.swmintl.com/role/Inventories">
        <link:definition>2120106 - Disclosure - Inventories</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="InventoriesTables" roleURI="http://www.swmintl.com/role/InventoriesTables">
        <link:definition>2321305 - Disclosure - Inventories (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="InventoriesDetails" roleURI="http://www.swmintl.com/role/InventoriesDetails">
        <link:definition>2422410 - Disclosure - Inventories (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="Goodwill" roleURI="http://www.swmintl.com/role/Goodwill">
        <link:definition>2123107 - Disclosure - Goodwill</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="GoodwillTables" roleURI="http://www.swmintl.com/role/GoodwillTables">
        <link:definition>2324306 - Disclosure - Goodwill (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="GoodwillDetails" roleURI="http://www.swmintl.com/role/GoodwillDetails">
        <link:definition>2425411 - Disclosure - Goodwill (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="IntangibleAssets" roleURI="http://www.swmintl.com/role/IntangibleAssets">
        <link:definition>2126108 - Disclosure - Intangible Assets</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="IntangibleAssetsTables" roleURI="http://www.swmintl.com/role/IntangibleAssetsTables">
        <link:definition>2327307 - Disclosure - Intangible Assets (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="IntangibleAssetsDetails" roleURI="http://www.swmintl.com/role/IntangibleAssetsDetails">
        <link:definition>2428412 - Disclosure - Intangible Assets (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="RestructuringandImpairmentActivities" roleURI="http://www.swmintl.com/role/RestructuringandImpairmentActivities">
        <link:definition>2129109 - Disclosure - Restructuring and Impairment Activities</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="RestructuringandImpairmentActivitiesTables" roleURI="http://www.swmintl.com/role/RestructuringandImpairmentActivitiesTables">
        <link:definition>2330308 - Disclosure - Restructuring and Impairment Activities (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="RestructuringandImpairmentActivitiesDetails" roleURI="http://www.swmintl.com/role/RestructuringandImpairmentActivitiesDetails">
        <link:definition>2431413 - Disclosure - Restructuring and Impairment Activities (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="RestructuringandImpairmentActivitiesRestructuringandrelatedchargesDetails" roleURI="http://www.swmintl.com/role/RestructuringandImpairmentActivitiesRestructuringandrelatedchargesDetails">
        <link:definition>2432414 - Disclosure - Restructuring and Impairment Activities - Restructuring and related charges (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="Debt" roleURI="http://www.swmintl.com/role/Debt">
        <link:definition>2133110 - Disclosure - Debt</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DebtTables" roleURI="http://www.swmintl.com/role/DebtTables">
        <link:definition>2334309 - Disclosure - Debt (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DebtScheduleofDebtSummarizedDetails" roleURI="http://www.swmintl.com/role/DebtScheduleofDebtSummarizedDetails">
        <link:definition>2435415 - Disclosure - Debt - Schedule of Debt Summarized (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DebtScheduleofDebtSummarizedDetails_1" roleURI="http://www.swmintl.com/role/DebtScheduleofDebtSummarizedDetails_1">
        <link:definition>2435415 - Disclosure - Debt - Schedule of Debt Summarized (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DebtAdditionalInformationDetails" roleURI="http://www.swmintl.com/role/DebtAdditionalInformationDetails">
        <link:definition>2436416 - Disclosure - Debt - Additional Information (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DebtScheduleofPrincipalRepaymentsDetails" roleURI="http://www.swmintl.com/role/DebtScheduleofPrincipalRepaymentsDetails">
        <link:definition>2437417 - Disclosure - Debt - Schedule of Principal Repayments (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="Derivatives" roleURI="http://www.swmintl.com/role/Derivatives">
        <link:definition>2138111 - Disclosure - Derivatives</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DerivativesTables" roleURI="http://www.swmintl.com/role/DerivativesTables">
        <link:definition>2339310 - Disclosure - Derivatives (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DerivativesAdditionalInformationDetails" roleURI="http://www.swmintl.com/role/DerivativesAdditionalInformationDetails">
        <link:definition>2440418 - Disclosure - Derivatives - Additional Information (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DerivativesDerivativesbyBalanceSheetLocationDetails" roleURI="http://www.swmintl.com/role/DerivativesDerivativesbyBalanceSheetLocationDetails">
        <link:definition>2441419 - Disclosure - Derivatives - Derivatives by Balance Sheet Location (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DerivativesDerivativeInstrumentsEffectonAOCIandResultsofOperationsDetails" roleURI="http://www.swmintl.com/role/DerivativesDerivativeInstrumentsEffectonAOCIandResultsofOperationsDetails">
        <link:definition>2442420 - Disclosure - Derivatives - Derivative Instruments Effect on AOCI and Results of Operations (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="DerivativesDerivativesDesignatedasCashFlowHedgesonNetIncomeDetails" roleURI="http://www.swmintl.com/role/DerivativesDerivativesDesignatedasCashFlowHedgesonNetIncomeDetails">
        <link:definition>2443421 - Disclosure - Derivatives - Derivatives Designated as Cash Flow Hedges on Net Income (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CommitmentsandContingencies" roleURI="http://www.swmintl.com/role/CommitmentsandContingencies">
        <link:definition>2144112 - Disclosure - Commitments and Contingencies</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="CommitmentsandContingenciesDetails" roleURI="http://www.swmintl.com/role/CommitmentsandContingenciesDetails">
        <link:definition>2445422 - Disclosure - Commitments and Contingencies (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="PostretirementandOtherBenefits" roleURI="http://www.swmintl.com/role/PostretirementandOtherBenefits">
        <link:definition>2146113 - Disclosure - Postretirement and Other Benefits</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="PostretirementandOtherBenefitsTables" roleURI="http://www.swmintl.com/role/PostretirementandOtherBenefitsTables">
        <link:definition>2347311 - Disclosure - Postretirement and Other Benefits (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="PostretirementandOtherBenefitsDetails" roleURI="http://www.swmintl.com/role/PostretirementandOtherBenefitsDetails">
        <link:definition>2448423 - Disclosure - Postretirement and Other Benefits (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="IncomeTaxes" roleURI="http://www.swmintl.com/role/IncomeTaxes">
        <link:definition>2149114 - Disclosure - Income Taxes</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="IncomeTaxesDetails" roleURI="http://www.swmintl.com/role/IncomeTaxesDetails">
        <link:definition>2450424 - Disclosure - Income Taxes (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="SegmentInformation" roleURI="http://www.swmintl.com/role/SegmentInformation">
        <link:definition>2151115 - Disclosure - Segment Information</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="SegmentInformationTables" roleURI="http://www.swmintl.com/role/SegmentInformationTables">
        <link:definition>2352312 - Disclosure - Segment Information (Tables)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
      <link:roleType id="SegmentInformationDetails" roleURI="http://www.swmintl.com/role/SegmentInformationDetails">
        <link:definition>2453425 - Disclosure - Segment Information (Details)</link:definition>
        <link:usedOn>link:presentationLink</link:usedOn>
        <link:usedOn>link:calculationLink</link:usedOn>
        <link:usedOn>link:definitionLink</link:usedOn>
      </link:roleType>
    </xs:appinfo>
  </xs:annotation>
  <xs:element id="swm_NewCreditFacilityMember" abstract="true" name="NewCreditFacilityMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_EngineeredPapersSegmentMember" abstract="true" name="EngineeredPapersSegmentMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_RawMaterialsAssessment2Member" abstract="true" name="RawMaterialsAssessment2Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_AnnualDebtAmortizationRateTermLoanFacility" abstract="false" name="AnnualDebtAmortizationRateTermLoanFacility" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="num:percentItemType"/>
  <xs:element id="swm_NatureOfBusinessLineItems" abstract="true" name="NatureOfBusinessLineItems" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:stringItemType"/>
  <xs:element id="swm_AdvancedMaterialsStructuresSegmentMember" abstract="true" name="AdvancedMaterialsStructuresSegmentMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_DebtInstrumentRedemptionPriceForEquityOfferingsPercentage" abstract="false" name="DebtInstrumentRedemptionPriceForEquityOfferingsPercentage" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="num:percentItemType"/>
  <xs:element id="swm_SeniorUnsecuredNotesDue2026Member" abstract="true" name="SeniorUnsecuredNotesDue2026Member" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_OtherAccrualsMember" abstract="true" name="OtherAccrualsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_SegmentNetSalesAbstract" abstract="true" name="SegmentNetSalesAbstract" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:stringItemType"/>
  <xs:element id="swm_EuropeandtheformerCommonwealthofIndependentStatesMember" abstract="true" name="EuropeandtheformerCommonwealthofIndependentStatesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_OtherForeignCountriesMember" abstract="true" name="OtherForeignCountriesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_UnallocatedMember" abstract="true" name="UnallocatedMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_NumberOfRevenueSources" abstract="false" name="NumberOfRevenueSources" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="swm_WriteDownValueSparePartsAndConsigmentInventory" abstract="false" name="WriteDownValueSparePartsAndConsigmentInventory" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="swm_IntangibleAssetsAccumulatedForeignExchangeGainLoss" abstract="false" name="IntangibleAssetsAccumulatedForeignExchangeGainLoss" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="swm_ElectricityAssessmentMember" abstract="true" name="ElectricityAssessmentMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_LongTermDebtMaturityAfterYearFour" abstract="false" name="LongTermDebtMaturityAfterYearFour" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="swm_MaterialConversionRevenuesMember" abstract="true" name="MaterialConversionRevenuesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_ElectricityAssessmentFourMember" abstract="true" name="ElectricityAssessmentFourMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_NumberOfAssessmentsFromTaxAuthoritiesRegardingIcmsTaxes" abstract="false" name="NumberOfAssessmentsFromTaxAuthoritiesRegardingIcmsTaxes" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="swm_ElectricityAssessmentOneMember" abstract="true" name="ElectricityAssessmentOneMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_NatureOfBusinessTable" abstract="true" name="NatureOfBusinessTable" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrldt:hypercubeItem" type="xbrli:stringItemType"/>
  <xs:element id="swm_ProductRevenuesMember" abstract="true" name="ProductRevenuesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_ElectricityAssessmentThreeMember" abstract="true" name="ElectricityAssessmentThreeMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_BrazilFranceAndUnitedStatesMember" abstract="true" name="BrazilFranceAndUnitedStatesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_RawMaterialsAssessmentAndRemainingElectricityAssessmentsMember" abstract="true" name="RawMaterialsAssessmentAndRemainingElectricityAssessmentsMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_OtherRevenuesMember" abstract="true" name="OtherRevenuesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_ConsolidatedMember" abstract="true" name="ConsolidatedMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_IntangibleAssetsAccumulatedImpairmentLoss" abstract="false" name="IntangibleAssetsAccumulatedImpairmentLoss" nillable="true" xbrli:periodType="instant" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="swm_AdjustmentsToAdditionalPaidInCapitalPlanModificationAdjustment" abstract="false" name="AdjustmentsToAdditionalPaidInCapitalPlanModificationAdjustment" nillable="true" xbrli:periodType="duration" xbrli:balance="credit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="swm_IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" abstract="false" name="IndefiniteLivedIntangibleAssetsExcludingGoodwillGross" nillable="true" xbrli:periodType="instant" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="swm_UsRevolverMember" abstract="true" name="UsRevolverMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_TermLoanFacilityMember" abstract="true" name="TermLoanFacilityMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_DebtInstrumentCovenantInterestCoverageRatio" abstract="false" name="DebtInstrumentCovenantInterestCoverageRatio" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:pureItemType"/>
  <xs:element id="swm_PensionAndOtherPostretirementBenefitExpenseNetOfPensionAndOtherPostretirementBenefitContributions" abstract="false" name="PensionAndOtherPostretirementBenefitExpenseNetOfPensionAndOtherPostretirementBenefitContributions" nillable="true" xbrli:periodType="duration" xbrli:balance="debit" substitutionGroup="xbrli:item" type="xbrli:monetaryItemType"/>
  <xs:element id="swm_TekraLLCAndTrientLLCMember" abstract="true" name="TekraLLCAndTrientLLCMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_NewCreditFacilityandBondIndentureMember" abstract="true" name="NewCreditFacilityandBondIndentureMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_DebtInstrumentCovenantEBITDARatio" abstract="false" name="DebtInstrumentCovenantEBITDARatio" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:pureItemType"/>
  <xs:element id="swm_SegmentOperatingProfitAbstract" abstract="true" name="SegmentOperatingProfitAbstract" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:stringItemType"/>
  <xs:element id="swm_ElectricityAssessmentTwoMember" abstract="true" name="ElectricityAssessmentTwoMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_NumberOfProductionLocations" abstract="false" name="NumberOfProductionLocations" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="swm_FrancePolandAndTheUnitedStatesMember" abstract="true" name="FrancePolandAndTheUnitedStatesMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_SalesRevenueNetPercentage" abstract="false" name="SalesRevenueNetPercentage" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="num:percentItemType"/>
  <xs:element id="swm_NumberOfJointVentures" abstract="false" name="NumberOfJointVentures" nillable="true" xbrli:periodType="instant" substitutionGroup="xbrli:item" type="xbrli:integerItemType"/>
  <xs:element id="swm_RawMaterialsAssessmentMember" abstract="true" name="RawMaterialsAssessmentMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_OperatingProfitPercentage" abstract="false" name="OperatingProfitPercentage" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="num:percentItemType"/>
  <xs:element id="swm_TradeNamesAndOtherMember" abstract="true" name="TradeNamesAndOtherMember" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="nonnum:domainItemType"/>
  <xs:element id="swm_LossContingencySettlementPeriod" abstract="false" name="LossContingencySettlementPeriod" nillable="true" xbrli:periodType="duration" substitutionGroup="xbrli:item" type="xbrli:durationItemType"/>
</xs:schema>
