Exhibit 5.1

[Letterhead of Sullivan & Cromwell LLP]

February 29, 2016

Unisys Corporation,

801 Lakeview Drive, Suite 100,

Blue Bell, Pennsylvania 19422.

Ladies and Gentlemen:

We are acting as counsel to Unisys Corporation, a Delaware corporation (the “Company”), in connection with the filing today by the Company of a post-effective amendment number 2 to the Company’s registration statement on Form S-3 (the “Amendment No. 2 to the Registration Statement”) under the Securities Act of 1933 (the “Act”). The Amendment No. 2 to the Registration Statement registers the following securities of the Company with an aggregate initial offering price not to exceed $700,000,000: (i) senior debt securities (the “Senior Debt Securities”) of the Company and subordinated debt securities (the “Subordinated Debt Securities” and, together with the Senior Debt Securities, the “Debt Securities”) of the Company; (ii) shares in one or more series of the Company’s preferred stock, par value $1.00 per share and in one or more series of the Company’s junior participating preferred stock (collectively, the “Preferred Stock”); (iii) shares in one or more series of the Company’s common stock, par value $0.01 per share (the “Common Stock”); (iv) warrants for the purchase of the Company’s Debt Securities, Preferred Stock or Common Stock (the “Warrants”); and (v) stock purchase contracts for the Company’s Common Stock or other securities (the “Stock Purchase Contracts”).

The Debt Securities, Preferred Stock, Common Stock, Warrants and Stock Purchase Contracts are referred to collectively as the “Securities”.

In connection with the filling of the Amendment No. 2 to the Registration Statement we, as your counsel, have examined such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion. Upon the basis of such examination, we advise you that, in our opinion:

(1) Debt Securities. When the applicable indenture relating to the Senior Debt Securities (the “Senior Debt Indenture”) has been duly authorized, executed and delivered, when the terms of the Senior Debt Securities and of their issuance and sale have been duly established in conformity with the Senior Debt Indenture so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, and when the Senior Debt Securities have been duly executed and authenticated in accordance with the Senior Debt Indenture and issued and sold as contemplated in the Amendment No. 2 to the Registration Statement, the Senior Debt Securities will constitute valid and legally binding obligations of the Company, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles. The Senior Debt Securities covered in the opinion in this paragraph include any Senior Debt Securities that may be issued upon exercise or pursuant to the terms of any Warrants that are exercisable for Senior Debt Securities. When the applicable indenture relating to the Subordinated Debt Securities (the “Subordinated Debt Indenture”) has been duly authorized, executed and delivered, when the terms of the Subordinated Debt Securities and of their issuance and sale have been duly established in conformity with the Subordinated Debt Indenture so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, and when the Subordinated Debt Securities have been duly executed and authenticated in accordance with the Subordinated Debt Indenture and issued and sold as contemplated in the Amendment No. 2 to the Registration Statement, the Subordinated Debt Securities will constitute valid and legally binding obligations of the Company, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles. The Subordinated Debt Securities covered in the opinion in this paragraph include any Subordinated Debt Securities that may be issued upon exercise or pursuant to the terms of any Warrant for Subordinated Debt Securities.

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(2) Preferred Stock. When the terms of the Preferred Stock and of its issuance and sale have been duly established in conformity with the Company’s Restated Certificate of Incorporation, and when the Preferred Stock has been duly issued and sold as contemplated by the Amendment No. 2 to the Registration Statement, and if all the foregoing actions are taken so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, the Preferred Stock will be validly issued, fully paid and nonassessable. The Preferred Stock covered in the opinion in this paragraph include any Preferred Stock that may be issued upon exercise or pursuant to the terms of any Warrant, Preferred Stock, Senior Debt Securities or Subordinated Debt Securities that are convertible into, or exercisable or exchangeable for, Preferred Stock or another series thereof.

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(3) Common Stock. When the terms of the Common Stock and of its issuance and sale have been duly established in conformity with the Company’s Restated Certificate of Incorporation, and when the Common Shares have been duly issued and sold as contemplated by the Amendment No. 2 to the Registration Statement, and if all the foregoing actions are taken so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding on the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company the Common Stock will be validly issued, fully paid and nonassessable. The Common Stock covered in the opinion in this paragraph include any Common Stock that may be issued upon exercise or pursuant to the terms of any Warrant, Preferred Stock, Senior Debt Securities or Subordinated Debt Securities that are convertible into, or exercisable or exchangeable for, Common Stock.

(4) Warrants. When the terms of the warrant agreement (the “Warrant Agreement”) under which the Warrants are to be issued have been duly established and the Warrant Agreement has been duly authorized, executed and delivered, when the terms of the Warrants and of their issuance and sale have been duly established in conformity with the Warrant Agreement and when such Warrants have been duly executed and authenticated in accordance with the Warrant Agreement and issued and sold as contemplated by the Amendment No. 2 to the Registration Statement, and if all the foregoing actions are taken pursuant to the authority granted in the Company and so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, such Warrants will constitute valid and legally binding obligations of the Company, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

(5) Stock Purchase Contracts. When the terms of the governing instrument or agreement under which of the Stock Purchase Contracts are to be issued have been duly established and the governing document has been duly executed and delivered, when the terms of such Stock Purchase Contracts and of their issuance and sale have been duly established in conformity with the applicable governing document and when such Stock Purchase Contracts have been duly executed, authenticated, issued and delivered in accordance with the applicable governing document and issued and sold as contemplated in the Amendment No. 2 to the Registration Statement, and if all the foregoing actions are taken pursuant to authority granted in the Company and so as not to violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and so as to comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, such Stock Purchase Contracts will constitute valid and legally binding obligations of the Company, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

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We note that, as of the date of this opinion, a judgment for money in an action based on a Security denominated in a foreign currency or currency unit in a Federal or state court in the United States ordinarily would be enforced in the United States only in United States dollars. The date used to determine the rate of conversion of the foreign currency or currency unit in which a particular Security is denominated into United States dollars will depend upon various factors, including which court renders the judgment. For example, a state court in the State of New York rendering a judgment on a Security denominated in a foreign currency would be required under Section 27 of the New York Judiciary Law to render such judgment in such foreign currency, and such judgment would be converted into United States dollars at the exchange rate prevailing on the date of entry of the judgment.

The foregoing opinion is limited to the Federal laws of the United States, the laws of the State of New York and the laws of the State of Delaware as in effect on the date of this letter, and we are expressing no opinion as to the effect of the laws of any other jurisdiction.

We have relied as to certain factual matters on information obtained from public officials, officers of the Company and other sources believed by us to be responsible. We have assumed, without independent verification, that all other governing documents under which the Securities are to be issued will have been duly authorized, executed and delivered by all parties thereto other than the Company and that the signatures on documents examined by us are genuine.

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In rendering the foregoing opinion, we are not passing upon, and assume no responsibility for, any disclosure in the Amendment No. 2 to the Registration Statement or any related prospectus regarding the Company, the Securities, or their offering and sale.

We hereby consent to the filing of this opinion as an exhibit to the Amendment No. 2 to the Registration Statement and to the reference to us under the heading “Legal Matters” in the Prospectus. 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 Act.

Very truly yours,

/s/ SULLIVAN & CROMWELL LLP