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

    <schemaVersion>X0305</schemaVersion>

    <documentType>4/A</documentType>

    <periodOfReport>2012-04-02</periodOfReport>

    <dateOfOriginalSubmission>2012-04-03</dateOfOriginalSubmission>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0001054721</issuerCik>
        <issuerName>BSQUARE CORP /WA</issuerName>
        <issuerTradingSymbol>BSQR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001275219</rptOwnerCik>
            <rptOwnerName>MAHAN SCOTT C</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>110 - 110TH AVE., NE</rptOwnerStreet1>
            <rptOwnerStreet2>SUITE 200</rptOwnerStreet2>
            <rptOwnerCity>BELLEVUE</rptOwnerCity>
            <rptOwnerState>WA</rptOwnerState>
            <rptOwnerZipCode>98004</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice Pres. Finance, CFO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2012-04-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>F</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>405</value>
                    <footnoteId id="F2"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>3.35</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>91156</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">The Form 4 is being amended to remove any reference to shares acquired on April 2, 2012 as the acquisition of all shares underlying the restricted stock unit grant was previously reported by the Reporting Person on the Form 4 filed on August 19, 2011.</footnote>
        <footnote id="F2">Represents shares that were withheld to pay the minimum tax liability for the restricted stock units that vested on April 2, 2012.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Scott C. Mahan</signatureName>
        <signatureDate>2012-04-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
