Exhibit 5.1

June 4, 2012

Unisys Corporation

801 Lakeview Drive

  Suite 100

Blue Bell, PA 19422

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as counsel to Unisys Corporation, a Delaware corporation (the “Company”), in connection with the Registration Statement on Form S-3 (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Securities Act”), relating to the Company’s (a) debt securities, which may be either senior (“Senior Debt Securities”) or subordinated (“Subordinated Debt Securities”) (collectively, the “Debt Securities”); (b) shares of common stock, par value $.01 per share (the “Common Stock”); (c) shares of preferred stock, par value $1 per share (the “Preferred Stock”); (d) warrants to purchase Debt Securities, Preferred Stock or Common Stock (the “Warrants”) and (e) contracts for the purchase and sale of shares of Common Stock or other securities (the “Purchase Contracts”). The Debt Securities, the Common Stock, the Preferred Stock, the Warrants and the Purchase Contracts are hereinafter collectively referred to as the “Securities.” The Securities may be issued and sold or delivered from time to time as set forth in the Registration Statement, any amendment thereto, the prospectus contained therein (the “Prospectus”) and supplements to the Prospectus pursuant to Rule 415 under the Securities Act in an indeterminate amount.

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The Senior Debt Securities will be issued under an Indenture (the “Senior Indenture”) between the Company and Wells Fargo Bank, National Association, as Trustee (the “Senior Trustee”). The Subordinated Debt Securities will be issued under an Indenture (the “Subordinated Indenture”) between the Company and Wells Fargo Bank, National Association, as Trustee (the “Subordinated Trustee”). The Senior Indenture and the Subordinated Indenture are hereinafter referred to collectively as the “Indentures.”

The Warrants relating to Common Stock or Preferred Stock will be issued under a warrant agreement between the Company and a warrant agent as shall be named therein. The Warrants relating to Senior Debt Securities will be issued under a warrant agreement among the Company, a warrant agent as shall be named therein and the Senior Trustee. The Warrants relating to Subordinated Debt Securities will be issued under a warrant agreement among the Company, a warrant agent as shall be named therein and the Subordinated Trustee. Such warrant agreements are hereinafter referred to collectively as the “Warrant Agreements.” Each party to a Warrant Agreement other than the Company is referred to hereinafter as a “Counterparty.”

The Purchase Contracts will be issued pursuant to a Purchase Contract Agreement (the “Purchase Contract Agreement”) between the Company and a purchase contract agent as shall be named therein (the “Purchase Contract Agent”).

We have examined the Registration Statement and (a) the Indentures, (b) the Company’s Restated Certificate of Incorporation, as amended, (c) the Company’s By-laws and (d) the form of the share certificate, which have been filed with the Commission as exhibits to

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the Registration Statement. We also have examined the originals, or duplicates or certified or conformed copies, of such records, agreements, documents and other instruments and have made such other investigations as we have deemed relevant and necessary in connection with the opinions hereinafter set forth. As to questions of fact material to this opinion, we have relied upon certificates or comparable documents of public officials and of officers and representatives of the Company.

In rendering the opinions set forth below, 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 also assumed that: (1) the Senior Indenture is the valid and legally binding obligation of the Senior Trustee; (2) the Subordinated Indenture is the valid and legally binding obligation of the Subordinated Trustee; (3) at the time of execution, countersignature, issuance and delivery of any Warrants, the related Warrant Agreement will be the valid and legally binding obligation of each Counterparty thereto and (4) at the time of execution, issuance and delivery of any Purchase Contracts, the related Purchase Contract Agreement will be the valid and legally binding obligation of the Purchase Contract Agent.

We have assumed further that at the time of execution, countersignature, issuance and delivery of any Warrants, the related Warrant Agreement will have been duly authorized, executed and delivered by the Company and at the time of execution, issuance and delivery of any Purchase Contracts, the related Purchase Contract Agreement will have been duly authorized, executed and delivered by the Company.

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

1. With respect to the Debt Securities, assuming (a) the taking of all necessary corporate action to approve the issuance and terms of any Debt Securities, the terms of the offering thereof and related matters by the Board of Directors of the Company, a duly constituted and acting committee of such Board or duly authorized officers of the Company (such Board of Directors, committee or authorized officers being referred to herein as the “Board”) and (b) the due execution, authentication, issuance and delivery of such Debt Securities, upon payment of the consideration therefor provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Board and otherwise in accordance with the provisions of the applicable Indenture and such agreement (and, in the case of Debt Securities issuable upon conversion or exercise of other Securities, in accordance with the terms of such Security or the instrument governing such Security providing for such conversion or exercise), such Debt Securities will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms.

2. With respect to the Common Stock, assuming (a) the taking by the Board of Directors of the Company of all necessary corporate action to authorize and approve the issuance of the Common Stock and (b) due issuance and delivery of the Common Stock, upon payment therefor in accordance with the applicable definitive purchase, underwriting or similar agreement approved by the Board of Directors of the Company (and, in the case of shares of Common Stock issuable upon conversion or exercise of other Securities, in accordance with the terms of such Security or the instrument governing such Security providing for such conversion or exercise), the Common Stock will be validly issued, fully paid and non-assessable.

3. With respect to the Preferred Stock, assuming (a) the taking by the Board of Directors of the Company of all necessary corporate action to authorize and approve the issuance of the Preferred Stock and to establish the terms thereof, (b) the due filing of an appropriate certificate of designations conforming to the Delaware General Corporation Law regarding such Preferred Stock with the Secretary of State of the State of Delaware and (c) the due issuance and delivery of the Preferred Stock, upon payment therefor in accordance with the applicable definitive purchase, underwriting or similar agreement approved by the Board of Directors of the Company (and, in the case of shares of Preferred Stock issuable upon conversion or exercise of other Securities, in accordance with the terms of such Security or the instrument governing such Security providing for such conversion or exercise), the Preferred Stock will be validly issued, fully paid and non-assessable.

4. With respect to the Warrants, assuming (a) the taking of all necessary corporate action by the Board of Directors of the Company to approve the execution and delivery of a related Warrant Agreement in the form to be filed as an exhibit to the Registration Statement and (b) the due execution, countersignature, issuance and delivery of such Warrants, upon payment of the consideration for such Warrants provided for in the applicable definitive purchase,

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underwriting or similar agreement approved by the Board of Directors of the Company and otherwise in accordance with the provisions of the applicable Warrant Agreement and such agreement, such Warrants will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms.

5. With respect to the Purchase Contracts, assuming (a) the taking of all necessary corporate action by the Board of Directors of the Company to authorize and approve the issuance of the Purchase Contracts and to establish the terms thereof, (b) the taking of all necessary corporate action by the Board of Directors of the Company to approve the execution and delivery of the related Purchase Contract Agreement and (c) the due execution, issuance and delivery of the Purchase Contracts, upon payment of the consideration for such Purchase Contracts provided for in the applicable definitive purchase, underwriting or similar agreement approved by the Board of Directors of the Company and otherwise in accordance with the provisions of the applicable Purchase Contract Agreement and such agreement, the Purchase Contracts will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms.

Our opinions set forth in paragraphs 1, 4 and 5 above are subject to the effects of (i) bankruptcy, insolvency, fraudulent conveyance, reorganization, moratorium and other similar laws relating to or affecting creditors’ rights generally, (ii) general equitable principles (whether considered in a proceeding in equity or at law) and (iii) an implied covenant of good faith and fair dealing.

We do not express any opinion herein concerning any law other than the law of the State of New York and the Delaware General Corporation Law.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the Registration Statement and to the use of our name under the caption “Legal Matters” in the Prospectus included in the Registration Statement.

Very truly yours,

/s/ SIMPSON THACHER & BARTLETT LLP

SIMPSON THACHER & BARTLETT LLP