<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-09-18</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000918646</issuerCik><issuerName>CENTEX CONSTRUCTION PRODUCTS INC</issuerName>        <issuerTradingSymbol>CXP</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001063775</rptOwnerCik><rptOwnerName>ROWLEY STEVE</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>2728 NORTH HARWOOD</rptOwnerStreet1><rptOwnerStreet2>SUITE 600</rptOwnerStreet2><rptOwnerCity>DALLAS</rptOwnerCity><rptOwnerState>TX</rptOwnerState><rptOwnerZipCode>75201</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>President &amp; CEO</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock</value><footnoteId id="F1" /></securityTitle><transactionDate><value>2003-09-18</value></transactionDate><deemedExecutionDate></deemedExecutionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>15000</value></transactionShares><transactionPricePerShare><value>0</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>15000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeHolding><securityTitle><value>Common Stock</value></securityTitle><postTransactionAmounts><sharesOwnedFollowingTransaction><value>1162</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By 401(k) Plan</value></natureOfOwnership></ownershipNature></nonDerivativeHolding></nonDerivativeTable><footnotes><footnote id="F1">This award will vest as follows:  6,428 shares on 9/18/06; 2,143 shares on 9/18/07; 2,143 shares on 9/18/08; 2,143 shares on 9/18/09 and 2,143 shares on 9/18/10.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/ Steven R. Rowley</signatureName><signatureDate>2003-09-22</signatureDate></ownerSignature></ownershipDocument>

