<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2020-10-07</periodOfReport>

    <issuer>
        <issuerCik>0000001750</issuerCik>
        <issuerName>AAR CORP</issuerName>
        <issuerTradingSymbol>AIR</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001554880</rptOwnerCik>
            <rptOwnerName>Holmes John McClain III</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>1100 N. WOOD DALE ROAD</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>WOOD DALE</rptOwnerCity>
            <rptOwnerState>IL</rptOwnerState>
            <rptOwnerZipCode>60191</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>1</isDirector>
            <isOfficer>1</isOfficer>
            <officerTitle>President &amp; CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <derivativeTable>
        <derivativeTransaction>
            <securityTitle>
                <value>Stock Option</value>
            </securityTitle>
            <conversionOrExercisePrice>
                <value>18.94</value>
            </conversionOrExercisePrice>
            <transactionDate>
                <value>2020-10-07</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>326600</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>18.94</value>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <exerciseDate>
                <value>2021-07-31</value>
                <footnoteId id="F2"/>
            </exerciseDate>
            <expirationDate>
                <value>2030-07-13</value>
            </expirationDate>
            <underlyingSecurity>
                <underlyingSecurityTitle>
                    <value>Common Stock</value>
                </underlyingSecurityTitle>
                <underlyingSecurityShares>
                    <value>326600</value>
                </underlyingSecurityShares>
            </underlyingSecurity>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>326600</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </derivativeTransaction>
    </derivativeTable>

    <footnotes>
        <footnote id="F1">On July 13, 2020, the reporting person was awarded 326,600 non-qualified stock options pursuant to AAR CORP. 2013 Stock Plan (as Amended and Restated Effective July 13, 2020) (the &quot;Plan&quot;).  The option grant was approved by the Company's Compensation Committee on July 13, 2020 subject to stockholder approval of the increase in shares issuable under the Plan, pursuant to which the option was granted.  The Company's stockholders approved the Plan on October 7, 2020.</footnote>
        <footnote id="F2">The awarded stock option vests and becomes exercisable in 1/3 annual installments beginning on July 31, 2021 and shall vest as follows: 33 and 1/3% on each of July 31, 2021, July 31, 2022 and July 31, 2023.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Kai England, Power of Attorney</signatureName>
        <signatureDate>2020-10-07</signatureDate>
    </ownerSignature>
</ownershipDocument>
