<?xml version="1.0"?><ownershipDocument><schemaVersion>X0101</schemaVersion>    <documentType>4</documentType><periodOfReport>2003-06-11</periodOfReport><issuer><issuerCik>0001002811</issuerCik><issuerName>KENSEY NASH CORP</issuerName>        <issuerTradingSymbol>KNSY</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001225164</rptOwnerCik><rptOwnerName>EVANS DOUGLAS G</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>COO</officerTitle><otherText></otherText></reportingOwnerRelationship></reportingOwner><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-06-11</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>25000</value></transactionShares><transactionValue><value>8.75</value></transactionValue><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>80050</value><footnoteId id="F1" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></nonDerivativeSecurity><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-06-11</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>25000</value></transactionShares><transactionValue><value>24</value></transactionValue><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>55050</value><footnoteId id="F3" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></nonDerivativeSecurity><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-06-11</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2200</value></transactionShares><transactionValue><value>8.75</value></transactionValue><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>57250</value><footnoteId id="F4" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></nonDerivativeSecurity><nonDerivativeSecurity><securityTitle><value>Common Stock</value></securityTitle><transactionDate><value>2003-06-11</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>S</transactionCode><equitySwapInvolved>0</equitySwapInvolved><footnoteId id="F2" /></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>2200</value></transactionShares><transactionValue><value>23</value></transactionValue><transactionAcquiredDisposedCode><value>D</value></transactionAcquiredDisposedCode></transactionAmounts><postTransactionAmounts><sharesOwnedFollowingTransaction><value>55050</value><footnoteId id="F3" /></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>I</value></directOrIndirectOwnership><natureOfOwnership><value>By Trust</value></natureOfOwnership></ownershipNature></nonDerivativeSecurity><derivativeSecurity><securityTitle><value>Employee Stock Options (rights to buy)</value></securityTitle><conversionOrExercisePrice><value>8.75</value></conversionOrExercisePrice><transactionDate><value>2003-06-11</value></transactionDate><transactionCoding><transactionFormType>4</transactionFormType><transactionCode>M</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionTimeliness><value></value></transactionTimeliness><transactionAmounts><transactionShares><value>27200</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>60000</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>60000</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership></ownershipNature></derivativeSecurity><footnotes><footnote id="F1">Of the total number of shares held, 25,000 shares are directly held, 55,050 shares are indirectly held. Of the shares indirectly held, 54,000 shares are held by the Douglas G. Evans Revocable Trust, of which the Reporting Person is Trustee, for the benefit of Reporting Person and his spouse and 1,050 shares were acquired by minor children of Reporting Person living in the same household as the Reporting Person.</footnote><footnote id="F2">The sales reported in this Form 4 were effected pursuant to a Rule 10b5-1 trading plan adopted by the reporting person in April 2002.</footnote><footnote id="F3">Of the total number of shares indirectly held, 54,000 shares are held by the Douglas G. Evans Revocable Trust, of which the Reporting Person is Trustee, for the benefit of Reporting Person and his spouse and 1,050 shares were acquired by minor children of Reporting Person living in the same household as the Reporting Person.</footnote><footnote id="F4">Of the total number of shares held, 2,200 shares are directly held, 55,050 shares are indirectly held. Of the shares indirectly held, 54,000 shares are held by the Douglas G. Evans Revocable Trust, of which the Reporting Person is Trustee, for the benefit of Reporting Person and his spouse and 1,050 shares were acquired by minor children of Reporting Person living in the same household as the Reporting Person.</footnote></footnotes><ownerSignature><signatureName>/s/ Douglas G. Evans, P.E.</signatureName><signatureDate>2003-06-13</signatureDate></ownerSignature></ownershipDocument>

