<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2015-11-16</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001227500</issuerCik>
        <issuerName>EQUITY BANCSHARES INC</issuerName>
        <issuerTradingSymbol>EQBK</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001656868</rptOwnerCik>
            <rptOwnerName>Goldstein Wayne K</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>7701 E KELLOGG DR., STE. 200</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WICHITA</rptOwnerCity>
            <rptOwnerState>KS</rptOwnerState>
            <rptOwnerZipCode>67207</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Class B Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2015-11-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>100000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>22.50</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>326788</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>By Endicott Opportunity Partners III, L.P.</value>
                    <footnoteId id="F1"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Consists of shares held by Endicott Opportunity Partners III, L.P. (&quot;EOPIII&quot;). Endicott Management Company is the investment manager to EOP III and consequently has the authority to vote and to dispose of the securities held by EOP III. W.R. Endicott III, L.L.C. (&quot;WRE III&quot;), is the general partner of EOP III and may be deemed to have beneficial ownership of, and share voting and dispositive power over, shares of securities held directly by EOP III. Mr. Goldstein is the Co-President and a shareholder of EMC and a managing member of WRE III and may be deemed to have beneficial ownership of, and share voting and dispositive over, securities held directly by EOP III. Mr. Goldstein disclaims beneficial ownership of these securities except to the extent of his pecuniary interest therein, and the inclusion of these shares in this report shall not be deemed an admission of beneficial ownership of the reported shares for purposes of Section 16 or for any other purpose.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Gregory H. Kossover, attorney-in-fact</signatureName>
        <signatureDate>2015-11-17</signatureDate>
    </ownerSignature>
</ownershipDocument>
