<?xml version="1.0"?><ownershipDocument><schemaVersion>X0201</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-08-05</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><issuer><issuerCik>0000807884</issuerCik><issuerName>CASH AMERICA INTERNATIONAL INC</issuerName>        <issuerTradingSymbol>PWN</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001186898</rptOwnerCik><rptOwnerName>FINN JERRY D</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>1600 W. 7TH STREET</rptOwnerStreet1><rptOwnerStreet2></rptOwnerStreet2><rptOwnerCity>FORT WORTH</rptOwnerCity><rptOwnerState>TX</rptOwnerState><rptOwnerZipCode>76102</rptOwnerZipCode><rptOwnerStateDescription></rptOwnerStateDescription></reportingOwnerAddress><reportingOwnerRelationship><isDirector>0</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>Exec. VP - Domestic Operations</officerTitle></reportingOwnerRelationship></reportingOwner><nonDerivativeTable><nonDerivativeTransaction><securityTitle><value>Common Stock par value $.10</value></securityTitle><transactionDate><value>2003-08-05</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>8350</value></transactionShares><transactionPricePerShare><value>10.8125</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>8500</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction><nonDerivativeTransaction><securityTitle><value>Common Stock par value $.10</value></securityTitle><transactionDate><value>2003-08-05</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>8350</value></transactionShares><transactionPricePerShare><value>16.7052</value></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>150</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeTransaction></nonDerivativeTable><derivativeTable><derivativeTransaction><securityTitle><value>Stock Options (right to buy)</value></securityTitle><conversionOrExercisePrice><value>10.8125</value></conversionOrExercisePrice><transactionDate><value>2003-08-05</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>8350</value></transactionShares><transactionPricePerShare><footnoteId id="F1" /></transactionPricePerShare><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>1998-06-01</value></exerciseDate><expirationDate><value>2007-09-30</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>8350</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>124700</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeTransaction></derivativeTable><footnotes><footnote id="F1">Not applicable.</footnote></footnotes><remarks></remarks><ownerSignature><signatureName>/s/  Jerry D. Finn</signatureName><signatureDate>2003-08-06</signatureDate></ownerSignature></ownershipDocument>

