<SUBMISSION>
<ACCESSION-NUMBER>0001209191-20-001276
<TYPE>4
<PUBLIC-DOCUMENT-COUNT>1
<PERIOD>20191231
<FILING-DATE>20200103
<DATE-OF-FILING-DATE-CHANGE>20200103
<REPORTING-OWNER>
<OWNER-DATA>
<CONFORMED-NAME>Krylov Sergei
<CIK>0001594869
</OWNER-DATA>
<FILING-VALUES>
<FORM-TYPE>4
<ACT>34
<FILE-NUMBER>001-33801
<FILM-NUMBER>20506982
</FILING-VALUES>
<MAIL-ADDRESS>
<STREET1>6500 WEST FREEWAY, 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>2019-12-31</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001594869</rptOwnerCik>
            <rptOwnerName>Krylov Sergei</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>ONE RIDGMAR CENTRE</rptOwnerStreet1>
            <rptOwnerStreet2>6500 WEST FREEWAY, SUITE 900</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>President and CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>D</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>103433</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>420996</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2019-12-31</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>27135</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>0.00</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>393861</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Shares granted on March 7, 2017 which were subject to the Issuer's three-year shareholder return (TSR) performance.  As of December 31, 2019, TSR metrics were not met and 103,433 shares were forfeited.</footnote>
        <footnote id="F2">Represents the tax liability on December 31, 2019 satisfied by withholding 27,135 shares incident to the vesting of securities under a Restricted Stock Award Agreement dated March 7, 2017 between the Reporting Person and the Issuer.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Joshua E. Dazey, attorney-in-fact</signatureName>
        <signatureDate>2020-01-03</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SUBMISSION>
