Chicago Bridge & Iron 8-K Cb&i Completes Shaw Group Acquisition

Exhibit 23.1

Consent of Independent Registered Public Accounting Firm

We consent to the incorporation by reference in the registration statements (No. 333-64442, 333-156004, 333-87081, 333-39975, 333-24443, 333-24445, 333-33199, 333-159182, 333-159183) on Form S-8 and registration statements (No. 333-160852 and 333-182223) on Form S-3 of Chicago Bridge & Iron Company N.V. of our report dated October 19, 2012, with respect to the consolidated balance sheets of The Shaw Group Inc. and subsidiaries as of August 31, 2012 and 2011, and the related consolidated statements of operations, comprehensive income (loss), shareholders’ equity, and cash flows for each of the years in the three-year period ended August 31, 2012, which report appears in the Form 8-K of Chicago Bridge & Iron Company N.V.

/s/ KPMG LLP

Baton Rouge, Louisiana

February 18, 2013