[Letter head of Skadden, Arps, Slate, Meagher & Flom LLP]

Exhibit 5.1

February 4, 2021

Triumph Group, Inc.

899 Cassatt Road, Suite 210

Berwyn, PA 19312

$150,000,000 At-the-Market Program for Common Stock

Ladies and Gentlemen:

We have acted as special United States counsel to Triumph Group, Inc., a Delaware corporation (the “Company” or “Our Client”), in connection with the Equity Distribution Agreement, dated February 4, 2021 (the “Equity Distribution Agreement”), among you as the manager (the “Manager”), and the Company, relating to the sale by the Company to or through the Manager, from time to time, of shares of the Company’s Common Stock, par value $0.001 per share (the “Shares”), with the Shares to be sold under the Equity Distribution Agreement not to exceed an aggregate gross sales price of $150,000,000 (the “Securities”).

This opinion is being furnished in accordance with the requirements of Item 601(b)(5) of Regulation S-K under the Securities Act of 1933, as amended (the “Securities Act”).

In rendering the opinions stated herein, we have examined and relied upon the following:

(a) the registration statement on Form S-3ASR (File No. 333-251429) of the Company relating to the Securities and other securities of the Company filed with the Securities and Exchange Commission (the “Commission”) on December 17, 2020 under the Securities Act, allowing for delayed offerings pursuant to Rule 415 of the General Rules and Regulations under the Securities Act (the “Rules and Regulations”), including information deemed to be a part of the registration statement pursuant to Rule 430B of the Rules and Regulations (such registration statement being hereinafter referred to as the “Registration Statement”);

(b) the prospectus, dated December 17, 2020 (the “Base Prospectus”), which forms a part of and is included in the Registration Statement;

Triumph Group, Inc.

February 4, 2021

Page 2

(c) the prospectus supplement, dated February 4, 2021 (together with the Base Prospectus, the “Prospectus”), relating to the offering of the Securities, in the form filed with the Commission pursuant to Rule 424(b) of the Rules and Regulations;

(d) an executed copy of the Equity Distribution Agreement;

(e) an executed copy of a certificate of Jennifer H. Allen, Senior Vice President, General Counsel and Secretary of the Company, dated the date hereof (the “Secretary’s Certificate”);

(f) a copy of the Amended and Restated Certificate of Incorporation of the Company, as amended by the Certificate of Amended and Restated Certificate of Incorporation of the Company, certified by the Secretary of State of the State of Delaware as of February 2, 2021, and certified pursuant to the Secretary’s Certificate (the “Certificate of Incorporation”);

(g) a copy of the Company’s By-laws, as amended and in effect as of the date hereof, certified pursuant to the Secretary’s Certificate (the “By-laws”);

(h) copies of certain resolutions of the Board of Directors of the Company, adopted on January 28, 2021, certified pursuant to the Secretary’s Certificate; and

(i) copies of certain resolutions of the Finance Committee of the Board of Directors of the Company, adopted on January 28, 2021, certified pursuant to the Secretary’s Certificate;

We have also examined originals or copies, certified or otherwise identified to our satisfaction, of such records of the Company and such agreements, certificates and receipts of public officials, certificates of officers or other representatives of the Company and others, and such other documents as we have deemed necessary or appropriate as a basis for the opinion stated below, including the facts and conclusions set forth in the Secretary’s Certificate and the factual representations and warranties contained in the Equity Distribution Agreement. We have assumed that the issuance of the Securities does not violate or conflict with any agreement or instrument binding on the Company (except that we do not make this assumption with respect to the Certificate of Incorporation or the Bylaws).

In our examination, we have assumed the genuineness of all signatures, including electronic signatures, the legal capacity and competency of all natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as facsimile, electronic, certified or photocopied copies, and the authenticity of the originals of such copies. As to any facts relevant to the opinions stated herein that we did not independently establish or verify, we have relied upon statements and representations of officers and other representatives of the Company and others and of public officials.

We do not express any opinion with respect to the laws of any jurisdiction other than the General Corporation Law of the State of Delaware (the “DGCL”). The Securities may be sold from time to time on a delayed or continuous basis, and this opinion is limited to the laws, including the rules and regulations, as in effect on the date hereof, which laws are subject to change with possible retroactive effect.

Triumph Group, Inc.

February 4, 2021

Page 3

Based upon the foregoing and subject to the qualifications and assumptions stated herein, we are of the opinion that:

1. The Securities have been duly authorized by all requisite corporate action on the part of the Company under the DGCL and when issued and sold in accordance with the terms of the Equity Distribution Agreement, will be validly issued, fully paid and nonassessable, provided that the consideration therefor is not less than $0.001 per share.

We hereby consent to the reference to our firm under the heading “Legal Matters” in the Prospectus. We also hereby consent to the filing of this opinion with the Commission as an exhibit to the Company’s Current Report on Form 8-K being filed on the date hereof and incorporated by reference into the Registration Statement. In giving this consent, we do not thereby admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act or the Rules and Regulations. This opinion is expressed as of the date hereof unless otherwise expressly stated, and we disclaim any undertaking to advise you of any subsequent changes in the facts stated or assumed herein or of any subsequent changes in applicable laws.

Very truly yours,

/s/ Skadden, Arps, Slate, Meagher & Flom LLP

MJZ