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 on Form 10-K of Triumph Group, Inc. (the "Company") for the year ended March 31, 2020, as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, Daniel J. Crowley, 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, to the best of my knowledge, that:

(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.

By:	/s/ Daniel J. Crowley
	Daniel J. Crowley President and Chief Executive Officer (Principal Executive Officer)
	May 28, 2020

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A signed original of this written statement required by Section 906 has been provided to Triumph Group, Inc. and will be retained by Triumph Group, Inc. and furnished to the Securities and Exchange Commission or its staff upon request.