American Eagle Outfitters (AEO) 10-K 2005 FY Annual 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 Annual Report of American Eagle Outfitters, Inc. on Form 10-K for the period ended January 29, 2005 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, James V. O’Donnell, Chief Executive Officer of American Eagle Outfitters, Inc., certify to the best of my knowledge, pursuant to 18 U.S.C. (S) 1350, as adopted pursuant to (S) 906 of the Sarbanes-Oxley Act of 2002, that:

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

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

/s/    JAMES V. O’DONNELL        

James V. O’Donnell

Chief Executive Officer

April 14, 2005