Exhibit 8.1

|  | 787 Seventh Avenue New York, NY 10019-6099 Tel: 212 728 8000 Fax: 212 728 8111

January 13, 2026

Ryerson Holding Corporation

227 W. Monroe St., 27th Floor

Chicago, Illinois 60606

Ladies and Gentlemen:

We have acted as your counsel in connection with the Merger, as defined and described in the Agreement and Plan of Merger dated as of October 28, 2025 (the “Merger Agreement”), by and among Ryerson Holding Corporation, a Delaware corporation (“Ryerson”), Crimson MS Corp., an Ohio corporation and a direct wholly owned subsidiary of Ryerson (“Merger Sub”), and Olympic Steel, Inc., an Ohio corporation (“Olympic Steel”). This opinion is being provided to you pursuant to Section 5.13(b) of the Merger Agreement. Unless otherwise indicated, each capitalized term used herein has the meaning ascribed to it in the Merger Agreement.

In connection with this opinion, we have examined the Merger Agreement, registration statement on Form S-4, which includes the Joint Proxy Statement/Prospectus (the “Joint Proxy Statement/Prospectus”), filed with the Securities and Exchange Commission, and such other documents as we have deemed necessary or appropriate in order to enable us to render our opinion. In such examination, we have assumed the genuineness of all signatures, the legal capacity of natural persons, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as duplicates or certified or conformed copies, and the authenticity of the originals of such latter documents. We have not, however, undertaken any independent investigation of any factual matter set forth in any of the foregoing. For purposes of this opinion, we have assumed, with your permission, (i) that the Merger will be consummated in the manner described in the Merger Agreement and the Joint Proxy Statement/Prospectus and (ii) that the representations to be made by Ryerson and Olympic Steel in their respective tax representation letters pursuant to Section 5.13(b) of the Merger Agreement in the forms attached as Exhibit C and Exhibit D of the Merger Agreement are true, correct and complete and will remain so until the Effective Time. We have also assumed that the parties have complied with and, to the extent applicable, will continue to comply with, the obligations, covenants, and agreements contained in the Merger Agreement. In addition, our opinion is based solely on the documents that we have examined, the additional information that we have obtained, and the representations to be made by Ryerson and Olympic Steel referred to above, which we have assumed will be true as of the Effective Time.

Based on the foregoing, and subject to the assumptions and qualifications set forth therein, it is our opinion that the Merger will be treated for United States federal income tax purposes as a reorganization within the meaning of Section 368(a) of the Code.

BRUSSELSCHICAGODALLASFRANKFURTHAMBURGHOUSTON LONDONLOS ANGELES

MILANMUNICHNEW YORKPALO ALTOPARISROMESAN FRANCISCOWASHINGTON

Ryerson Holding Corporation

January 13, 2026

Page 2

Our opinion is based on the Code, Treasury Regulations, administrative pronouncements and judicial precedents in effect as of the date hereof, all of which are subject to change at any time. In addition, our opinions are based solely on the documents that we have examined and the statements contained in the representation letters referred to above. Our opinion cannot be relied upon if any of the facts pertinent to the U.S. federal income tax treatment of the Merger stated in such document are, or later become, inaccurate or if any of the statements contained in the representation letters referred to above are, or later become, inaccurate.

We express our opinion herein only as to those matters specifically set forth above and no opinion should be inferred as to the tax consequences of the Merger under any state, local or non-U.S. law, or with respect to other areas of U.S. federal taxation. We are members of the Bar of the State of New York, and we do not express any opinion herein concerning any law other than the federal law of the United States.

This opinion is furnished to you solely for use in connection with the Merger. This opinion may not be relied upon by you for any other purpose or relied upon or furnished to any other person without our prior written consent. We hereby consent to the filing of this opinion with the Securities and Exchange Commission as an exhibit to the Joint Proxy Statement/Prospectus and to the references therein to us. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act of 1933, as amended.

Very truly yours, /s/ Willkie Farr & Gallagher LLP