AAR (AIR) 10-K 2009 FY Annual report

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 Statement Nos. 333-152594, 333-122111, 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. 333-155911, 333-133692 and 333-114855 on Form S-3 of AAR CORP. of our reports dated July 15, 2009, with respect to the consolidated balance sheets of AAR CORP. and subsidiaries as of May 31, 2009 and 2008, 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, 2009, and the effectiveness of internal control over financial reporting as of May 31, 2009, which reports appear in the May 31, 2009 annual report on Form 10-K of AAR CORP.

(Signed) KPMG LLP

Chicago, Illinois

July 15, 2009