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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2018-08-17</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

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

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001574629</rptOwnerCik>
            <rptOwnerName>Vardeman Ryan L.</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>5310 HARVEST HILL ROAD, SUITE 110</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>DALLAS</rptOwnerCity>
            <rptOwnerState>TX</rptOwnerState>
            <rptOwnerZipCode>75230</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, No Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2018-08-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>98000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.95</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1046500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F1"/>
                    <footnoteId id="F2"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, No Par Value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16667</value>
                    <footnoteId id="F3"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This statement is filed by and on behalf of Ryan L. Vardeman. Palogic Value Fund, L.P., a Delaware limited partnership (&quot;Palogic Value Fund&quot;), and Mr. Vardeman are the record and direct beneficial owners of the securities covered by this statement. Palogic Value Management, L.P., a Delaware limited partnership (&quot;Palogic Value Management&quot;), is the general partner of, and may be deemed to beneficially own securities owned by, Palogic Value Fund. Palogic Capital Management, LLC, a Delaware limited liability company (&quot;Palogic Capital Management&quot;), is the general partner of, and may be deemed to beneficially own securities beneficially owned by, Palogic Value Management. Mr. Vardeman is the sole member of, and may be deemed to beneficially own securities beneficially owned by, Palogic Capital Management. Mr. Vardeman is also a limited partner in, and may be deemed to beneficially own securities owned by, Palogic Value Fund.</footnote>
        <footnote id="F2">The reporting person states that neither the filing of this statement nor anything herein shall be deemed an admission that the reporting person is, for purposes of Section 16 of the Securities Exchange Act of 1934, as amended or otherwise, the beneficial owner of any securities covered by this statement. The reporting person disclaims beneficial ownership of the securities covered by this statement, except to the extent of the pecuniary interest of the reporting person in such securities.</footnote>
        <footnote id="F3">Represents restricted stock units of BSQUARE Corporation, a Washington corporation (the &quot;Issuer&quot;), awarded to Ryan L. Vardeman on June 25, 2018 pursuant to the Issuer's compensation plan for non-employee directors and the Fourth Amended and Restated Stock Plan of the Issuer. The restricted stock units will vest quarterly in equal installments over one year following the date of the award.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ryan L. Vardeman</signatureName>
        <signatureDate>2018-08-21</signatureDate>
    </ownerSignature>
</ownershipDocument>
