Exhibit 5.1

May 12, 2014

The Babcock & Wilcox Company

13024 Ballantyne Corporate Place, Suite 700

Charlotte, North Carolina 28277

Ladies and Gentlemen:

We have acted as counsel for The Babcock & Wilcox Company, a Delaware corporation (the “Company”), in connection with the registration of 2,300,000 shares (the “Shares”) of the Company’s Common Stock, par value $0.01 per share, pursuant to the 2010 Long-Term Incentive Plan of The Babcock & Wilcox Company, as amended and restated (the “Plan”). In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of this opinion. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that the Shares that may be issued or delivered and sold pursuant to the Plan and the authorized forms of stock option, restricted stock unit or other applicable award agreements thereunder will be, when issued or delivered and sold in accordance with the Plan and such agreements, validly issued, fully paid and nonassessable, provided that the consideration for such Shares is at least equal to the stated par value thereof.

The opinion expressed herein is limited to the General Corporation Law of the State of Delaware, as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction. In addition, we have assumed that the resolutions authorizing the Company to issue or deliver and sell the Shares pursuant to the Plan and the applicable award agreements will be in full force and effect at all times at which such Shares are issued or delivered or sold by the Company, and the Company will take no action inconsistent with such resolutions.

In rendering the opinion above, we have assumed that each award under the Plan will be approved by the Board of Directors of the Company or an authorized committee of the Board of Directors.

May 12, 2014

The Babcock & Wilcox Company

Page 2

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement on Form S-8 filed by the Company to effect registration of the Shares to be issued and sold pursuant to the Plan under the Securities Act of 1933 (the “Act”). In giving such consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ JONES DAY