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

    <schemaVersion>X0508</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2025-11-05</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>Chairman, President &amp; CEO</officerTitle>
        </reportingOwnerRelationship>
    </reportingOwner>

    <aff10b5One>1</aff10b5One>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Common Stock</value>
            </securityTitle>
            <transactionDate>
                <value>2025-11-05</value>
            </transactionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness></transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>38462</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>83.501</value>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>260141</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Transaction in accordance with 10b5-1 trading plan adopted by John M. Holmes on Aug. 6, 2025.</footnote>
        <footnote id="F2">The price reported in column 4 is a weighted average price. These shares were sold in multiple transactions at prices ranging from $82.1200 to $85.1399 inclusive. The reporting person undertakes to provide AAR CORP., any security holder of AAR CORP., or the staff of the Securities and Exchange Commission upon request, full information regarding the number of shares sold at each separate price within the range set forth in this footnote.</footnote>
    </footnotes>

    <ownerSignature>
        <signatureName>/s/ Katherine Kwiat, power of attorney</signatureName>
        <signatureDate>2025-11-06</signatureDate>
    </ownerSignature>
</ownershipDocument>
