AAR (AIR) 10-Q 2006 Q1 Quarterly report

Exhibit 32.1

CERTIFICATION PURSUANT TO 18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the AAR CORP. (the “Company”) quarterly report on Form 10-Q for the period ending August 31, 2005 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, David P. Storch, Chief Executive Officer of the Company, certify pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to the best of my knowledge:

1.             The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934, as amended; and

2.             The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date:   October 5, 2005

 /s/ DAVID P. STORCH

 David P. Storch

 President and Chief Executive Officer