<SUBMISSION>
<ACCESSION-NUMBER>0001209191-18-053381
<TYPE>4
<PUBLIC-DOCUMENT-COUNT>1
<PERIOD>20181001
<FILING-DATE>20181002
<DATE-OF-FILING-DATE-CHANGE>20181002
<REPORTING-OWNER>
<OWNER-DATA>
<CONFORMED-NAME>Kahn Matthew
<CIK>0001696059
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>001-33801
<FILM-NUMBER>181102955
</FILING-VALUES>
<MAIL-ADDRESS>
<STREET1>36 BRUSH HILL ROAD
<CITY>NEWTON
<STATE>MA
<ZIP>02461
</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>2018-10-01</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001696059</rptOwnerCik>
            <rptOwnerName>Kahn Matthew</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>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2018-10-01</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>5813</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>5813</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>66648</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>by MRSAKAHN, LLC</value>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Represents shares of the issuer's common stock awarded to the reporting person for payment of director fees.</footnote>
        <footnote id="F2">The reporting person is the sole member of MRSAKAHN, LLC.  MRSAKAHN, LLC acquired shares solely as a result of a change in form of beneficial ownership.</footnote>
        <footnote id="F3">Excludes all shares previously reported as being held directly by the reporting person, which the reporting person contributed to MRSAKAHN, LLC.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ J. Curtis Henderson, attorney-in-fact</signatureName>
        <signatureDate>2018-10-02</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SUBMISSION>
