Exhibit 5.1

August 22, 2012

Unisys Corporation

801 Lakeview Drive

Suite 100

Blue Bell, Pennsylvania 19422

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 (File No. 333-181874) (the “Registration Statement”) filed by the Company with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), relating to the issuance thereunder by the Company of $210,000,000 aggregate principal amount of 6.25% Senior Notes due 2017 (the “Notes”). The Notes will be issued pursuant to the Indenture, dated as of June 1, 2012 (the “Base Indenture”), between the Company and Wells Fargo Bank, National Association, as trustee (the “Trustee”), as supplemented by the First Supplemental Indenture dated as of August 21, 2012 (together with the Base Indenture, the “Indenture”).

We have examined the Registration Statement as it became effective under the Act; the prospectus dated June 4, 2012 (the “Base Prospectus”), as supplemented by the prospectus supplement dated August 16, 2012 (the “Final Prospectus Supplement”), filed by the Company pursuant to Rule 424(b) of the rules and regulations of the Commission under the Act; the Indenture; duplicates of the global note representing the Notes; and the Underwriting Agreement dated August 21, 2012 (the “Underwriting Agreement”), among the Company and the underwriters named therein.

-2- August 22, 2012

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 opinion 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 opinion 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 also have assumed that the Indenture will be the valid and legally binding obligation of the Trustee.

Based upon the foregoing, and subject to the qualifications, assumptions and limitations stated herein, we are of the opinion that, assuming due authentication of the Notes by the Trustee, and upon payment and delivery in accordance with the Underwriting Agreement, the Notes will constitute valid and legally binding obligations of the Company, enforceable against the Company in accordance with their terms.

Our opinion set forth above is subject to (i) the effects of 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.

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

We hereby consent to the filing of this opinion letter as an Exhibit to the Current Report on Form 8-K dated the date hereof, which we understand will be incorporated by reference into the Registration Statement and to the use of our name under the captions “Validity of Securities” in the Final Prospectus Supplement and “Legal Matters” in the Base Prospectus, which are part of the Registration Statement.

Very truly yours,

/s/ SIMPSON THACHER & BARTLETT LLP

SIMPSON THACHER & BARTLETT LLP