<?xml version="1.0"?><ownershipDocument><schemaVersion>X0101</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-05-22</periodOfReport><issuer><issuerCik>0001002811</issuerCik><issuerName>KENSEY NASH CORP</issuerName>        <issuerTradingSymbol>KNSY</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001225166</rptOwnerCik><rptOwnerName>KAUFMANN JOSEPH W</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>  </rptOwnerStreet1><rptOwnerStreet2>  </rptOwnerStreet2><rptOwnerCity>  </rptOwnerCity><rptOwnerState>  </rptOwnerState><rptOwnerZipCode>  </rptOwnerZipCode></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>1</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle>CEO &amp; President</officerTitle><otherText></otherText></reportingOwnerRelationship></reportingOwner><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-05-22</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>50000</value></transactionShares><transactionValue><value>8.75</value></transactionValue><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>215833</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeSecurity><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-05-22</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>50000</value></transactionShares><transactionValue><value>21.25</value></transactionValue><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>165833</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></nonDerivativeSecurity><derivativeSecurity><securityTitle><value>Employee Stock Options (rights to buy)</value></securityTitle><conversionOrExercisePrice><value>8.75</value></conversionOrExercisePrice><transactionDate><value>2003-05-22</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>50000</value></transactionShares><transactionValue><value>8.75</value></transactionValue><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>1999-05-09</value></exerciseDate><expirationDate><value>2005-05-09</value></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>35600</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>35600</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeSecurity><footnotes></footnotes><ownerSignature><signatureName>/s/Douglas G. Evans, by power of attorney</signatureName><signatureDate>2003-05-22</signatureDate></ownerSignature></ownershipDocument>

