<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>3</documentType><periodOfReport>2003-07-24</periodOfReport><noSecuritiesOwned>1</noSecuritiesOwned><issuer><issuerCik>0001054721</issuerCik><issuerName>BSQUARE CORP /WA</issuerName>        <issuerTradingSymbol>BSQR</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001257013</rptOwnerCik><rptOwnerName>BIBEAULT DONALD B</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>3150 - 139TH AVE., SE</rptOwnerStreet1><rptOwnerStreet2>SUITE 500</rptOwnerStreet2><rptOwnerCity>BELLEVUE</rptOwnerCity><rptOwnerState>WA</rptOwnerState><rptOwnerZipCode>98005</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther></reportingOwnerRelationship></reportingOwner><footnotes></footnotes><remarks></remarks><ownerSignature><signatureName>Meena Kang Latta as Attorney-in-Fact for Donald B. Bibeault</signatureName><signatureDate>2003-07-28</signatureDate></ownerSignature></ownershipDocument>

