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Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

The Board of Directors
AAR CORP.:

We consent to the incorporation by reference in Registration Statements Nos. 333-112654, 33-19767, 333-102416, 333-81790, 333-54178, 333-95433, 333-71067, 333-44693, 333-38671, 33-26783, 33-38042, 33-43839, 33-58456, 33-56023, 33-57753, 333-15327, 333-22175, 333-26093, 333-00205, 002-89735 and 002-95635 on Form S-8 and in Registration Statement Nos. 333-114855 and 333-52853 on Form S-3 of AAR CORP. of our report dated June 28, 2004 relating to the consolidated balance sheets of AAR CORP. and subsidiaries as of May 31, 2004 and 2003 and the related consolidated statements of operations, stockholders' equity and cash flows for each of the years in the three-year period ended May 31, 2004, which report appears in the May 31, 2004 annual report on Form 10-K of AAR CORP.

KPMG LLP

Chicago, Illinois
July 20, 2004

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Exhibit 23.1