<SUBMISSION>
<ACCESSION-NUMBER>0001209191-18-062696
<TYPE>4
<PUBLIC-DOCUMENT-COUNT>1
<PERIOD>20181213
<FILING-DATE>20181214
<DATE-OF-FILING-DATE-CHANGE>20181214
<REPORTING-OWNER>
<OWNER-DATA>
<CONFORMED-NAME>Shaw Ian M.
<CIK>0001733488
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>001-33801
<FILM-NUMBER>181235691
</FILING-VALUES>
<MAIL-ADDRESS>
<STREET1>6500 WEST FREEWAY
<STREET2>SUITE 800
<CITY>FORT WORTH
<STATE>TX
<ZIP>76116
</MAIL-ADDRESS>
</REPORTING-OWNER>
<ISSUER>
<COMPANY-DATA>
<CONFORMED-NAME>Approach Resources Inc
<CIK>0001405073
<ASSIGNED-SIC>1311
<IRS-NUMBER>510424817
<STATE-OF-INCORPORATION>DE
<FISCAL-YEAR-END>1231
</COMPANY-DATA>
<BUSINESS-ADDRESS>
<STREET1>ONE RIDGMAR CENTRE
<STREET2>6500 WEST FREEWAY, SUITE 800
<CITY>FORT WORTH
<STATE>TX
<ZIP>76116
<PHONE>8179899000
</BUSINESS-ADDRESS>
<MAIL-ADDRESS>
<STREET1>ONE RIDGMAR CENTRE
<STREET2>6500 WEST FREEWAY, SUITE 800
<CITY>FORT WORTH
<STATE>TX
<ZIP>76116
</MAIL-ADDRESS>
</ISSUER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc4.xml
<DESCRIPTION>FORM 4 SUBMISSION
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-12-13</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001405073</issuerCik>
        <issuerName>Approach Resources Inc</issuerName>
        <issuerTradingSymbol>AREX</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001733488</rptOwnerCik>
            <rptOwnerName>Shaw Ian M.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE RIDGMAR CENTRE</rptOwnerStreet1>
            <rptOwnerStreet2>6500 WEST FREEWAY, SUITE 800</rptOwnerStreet2>
            <rptOwnerCity>FORT WORTH</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>76116</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Chief Accounting Officer</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-12-13</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>20000</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.25</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>51340</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Includes 7,599 fully vested shares granted under the Issuer's 2018 Long Term Incentive Plan, in lieu of partial year-end cash bonus, as reported on Form 4 filed December 3, 2018.  The remainder shares were sold for tax and planning purposes.  The 20,000 shares were sold in multiple transactions, all at a price of $1.25 per share.  Mr. Shaw hereby undertakes to provide to the Securities and Exchange Commission staff, the issuer or any security holder of the issuer, upon request, full information regarding the number of shares and price at which the transaction was effected.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ J. Curtis Henderson, attorney-in-fact</signatureName>
        <signatureDate>2018-12-14</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SUBMISSION>
