<ownershipDocument><schemaVersion>X0101</schemaVersion>    <documentType>5</documentType><periodOfReport>2003-05-31</periodOfReport><notSubjectToSection16>0</notSubjectToSection16><form3HoldingsReported>0</form3HoldingsReported><form4TransactionsReported>0</form4TransactionsReported><issuer><issuerCik>0000001750</issuerCik><issuerName>AAR CORP</issuerName>        <issuerTradingSymbol>AIR</issuerTradingSymbol></issuer><reportingOwner><reportingOwnerId><rptOwnerCik>0001017982</rptOwnerCik><rptOwnerName>GOODWIN JAMES E</rptOwnerName></reportingOwnerId><reportingOwnerAddress><rptOwnerStreet1>  </rptOwnerStreet1><rptOwnerStreet2>  </rptOwnerStreet2><rptOwnerCity>  </rptOwnerCity><rptOwnerState>  </rptOwnerState><rptOwnerZipCode>  </rptOwnerZipCode></reportingOwnerAddress><reportingOwnerRelationship><isDirector>1</isDirector><isOfficer>0</isOfficer><isTenPercentOwner>0</isTenPercentOwner><isOther>0</isOther><officerTitle></officerTitle><otherText></otherText></reportingOwnerRelationship></reportingOwner><derivativeSecurity><securityTitle><value>Phantom Stock Units</value></securityTitle><conversionOrExercisePrice><value>11.44</value></conversionOrExercisePrice><transactionDate><value>2002-06-01</value></transactionDate><transactionCoding><transactionFormType>5</transactionFormType><transactionCode>A</transactionCode><equitySwapInvolved>0</equitySwapInvolved></transactionCoding><transactionAmounts><transactionShares><value>611</value></transactionShares><transactionValue><value>11.44</value></transactionValue><transactionAcquiredDisposedCode><value>A</value></transactionAcquiredDisposedCode></transactionAmounts><exerciseDate><value>2002-06-01</value></exerciseDate><expirationDate><value>2012-06-01</value><footnoteId id="F1"/></expirationDate><underlyingSecurity><underlyingSecurityTitle><value>Common Stock</value></underlyingSecurityTitle><underlyingSecurityShares><value>611</value></underlyingSecurityShares></underlyingSecurity><postTransactionAmounts><sharesOwnedFollowingTransaction><value>611</value></sharesOwnedFollowingTransaction></postTransactionAmounts><ownershipNature><directOrIndirectOwnership><value>D</value></directOrIndirectOwnership><natureOfOwnership><value></value></natureOfOwnership></ownershipNature></derivativeSecurity><footnotes><footnote id="F1">Phantom stock units are payable in stock on a 1-for-1 basis or cash at the grantee's election upon retirement/termination as a director.</footnote></footnotes><ownerSignature><signatureName>Jo-Ellen Kiddie</signatureName><signatureDate>2003-07-09</signatureDate></ownerSignature></ownershipDocument>

