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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2019-05-16</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>2019-05-16</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>61205</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.5064</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1107705</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, No Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2019-05-17</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>38795</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.4954</value>
                    <footnoteId id="F4"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1146500</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, No Par Value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>16667</value>
                    <footnoteId id="F5"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">This price represents the approximate weighted average price per share of common stock of BSQUARE Corporation, a Washington corporation (the &quot;Issuer&quot;), no par value (&quot;Shares&quot;), of purchases that were executed at prices ranging from $1.46 to $1.51 per Share.  The reporting person undertakes to provide, upon request by the Securities and Exchange Commission staff, the Issuer or a security holder of the Issuer, full information regarding the price per Share and the number of Shares purchased at each price.</footnote>
        <footnote id="F2">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="F3">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="F4">This price represents the approximate weighted average price per Share of purchases that were executed at prices ranging from $1.44 to $1.51 per Share.  The reporting person undertakes to provide, upon request by the Securities and Exchange Commission staff, the Issuer or a security holder of the Issuer, full information regarding the price per Share and the number of Shares purchased at each price.</footnote>
        <footnote id="F5">Includes 4,167 restricted stock units of the Issuer 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. These restricted stock units will vest on June 25, 2019.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>/s/ Ryan L. Vardeman</signatureName>
        <signatureDate>2019-05-20</signatureDate>
    </ownerSignature>
</ownershipDocument>
