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

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-03-02</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>1</isOther>
            <otherText>Member of 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001387846</rptOwnerCik>
            <rptOwnerName>Palogic Value Fund, LP</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Member of 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001532943</rptOwnerCik>
            <rptOwnerName>Palogic Value Management, L.P.</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Member of 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001494018</rptOwnerCik>
            <rptOwnerName>Palogic Capital Management, LLC</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>0</isDirector>
            <isOfficer>0</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>1</isOther>
            <otherText>Member of 10% Group</otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, No Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2020-03-02</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10761</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.2368</value>
                    <footnoteId id="F1"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1353508</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock, No Par Value</value>
            </securityTitle>
            <transactionDate>
                <value>2020-03-03</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>P</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>10000</value>
                </transactionShares>
                <transactionPricePerShare>
                    <value>1.2456</value>
                    <footnoteId id="F6"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>1363508</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>See Footnotes</value>
                    <footnoteId id="F2"/>
                    <footnoteId id="F3"/>
                    <footnoteId id="F4"/>
                    <footnoteId id="F5"/>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Common Stock, No Par Value</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>51389</value>
                    <footnoteId id="F7"/>
                </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 $1.21 to $1.25 per Share. The reporting persons undertake 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 jointly filed by and on behalf of each of Ryan L. Vardeman, Palogic Value Fund, L.P., a Delaware limited partnership (&quot;Palogic Value Fund&quot;), Palogic Value Management, L.P., a Delaware limited partnership (&quot;Palogic Value Management&quot;), and Palogic Capital Management, LLC, a Delaware limited liability company (&quot;Palogic Capital Management&quot;). Mr. Vardeman and Palogic Value Fund are the record and direct beneficial owners of the securities covered by this statement. Palogic Value Management is the general partner of, and may be deemed to beneficially own securities owned by, Palogic Value Fund.  Palogic Capital Management is the general partner of, and may be deemed to beneficially own securities beneficially owned by, Palogic Value Management.</footnote>
        <footnote id="F3">(continued from Footnote 2) 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="F4">The reporting persons state that neither the filing of this statement nor anything herein shall be deemed an admission that the reporting persons are, for purposes of Section 16 of the Securities Exchange Act of 1934, as amended (the &quot;Exchange Act&quot;) or otherwise, the beneficial owners of any securities covered by this statement. The reporting persons disclaim beneficial ownership of the securities covered by this statement, except to the extent of the pecuniary interest of the reporting persons in such securities.</footnote>
        <footnote id="F5">The reporting persons may be deemed to be a member of a group with respect to the Issuer or securities of the Issuer for purposes of Section 13(d) or 13(g) of the Exchange Act. The reporting persons declare that neither the filing of this statement nor anything herein shall be construed as an admission that such persons are, for the purposes of Section 13(d) or 13(g) of the Exchange Act or any other purpose, a member of a group with respect to the Issuer or securities of the Issuer.</footnote>
        <footnote id="F6">This price represents the approximate weighted average price per Share of purchases that were executed at prices ranging from $1.21 to $1.25 per Share. The reporting persons undertake 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="F7">Includes 17,361 restricted stock units of the Issuer awarded to Ryan L. Vardeman on June 11, 2019, pursuant to the Issuer's compensation plan for non-employee directors and the Fourth Amended and Restated Stock Plan of the Issuer which have not yet vested.</footnote>
    </footnotes>

    <remarks>Exhibit Index
Exhibit 99.1 - Joint Filer Information (filed herewith)
Exhibit 99.2 - Joint Filing Agreement (filed herewith)</remarks>

    <ownerSignature>
        <signatureName>RYAN L. VARDEMAN, By: /s/ Ryan L. Vardeman</signatureName>
        <signatureDate>2020-03-04</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>PALOGIC VALUE FUND, L.P., By: Palogic Value Management, L.P., Its: General Partner, By: Palogic Capital Management, LLC, Its: General Partner, By: /s/ Ryan L. Vardeman, Name: Ryan L. Vardeman, Title: Sole Member</signatureName>
        <signatureDate>2020-03-04</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>PALOGIC VALUE MANAGEMENT, L.P., By: Palogic Capital Management, LLC, Its: General Partner, By: /s/ Ryan L. Vardeman, Name: Ryan L. Vardeman, Title: Sole Member</signatureName>
        <signatureDate>2020-03-04</signatureDate>
    </ownerSignature>

    <ownerSignature>
        <signatureName>PALOGIC CAPITAL MANAGEMENT, LLC, By: /s/ Ryan L. Vardeman, Name: Ryan L. Vardeman, Title: Sole Member</signatureName>
        <signatureDate>2020-03-04</signatureDate>
    </ownerSignature>
</ownershipDocument>
