The Boeing Company (BA) 10-Q 2005 Q2 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 Quarterly Report of The Boeing Company (the Company) on Form 10-Q for the period ending June 30, 2005, as filed with the Securities and Exchange Commission on the date hereof (the Report), I, W. James McNerney, Jr., Chairman, President and Chief Executive Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 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 and 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 the Company.

/s/    W. James McNerney, Jr.

W. James McNerney, Jr.

Chairman, President and

Chief Executive Officer

July 27, 2005

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