1 Exhibit 23.1 Consent of Independent Accountants We hereby consent to the incorporation by reference in the Prospectus constituting part of the Registration Statement on Form S-3 (No. 333-42325) and in the Registration Statements on Form S-8 (Nos. 2-65727, 2-80553, 2-90910, 2-94151, 33-10381, 33-32109, 33-40246, 33-43925, 333-34489, 333-38291 and 333-38293) of Mallinckrodt Inc., of our report dated July 31, 1996 relating to the consolidated financial statements of Nellcor Puritan Bennett Incorporated, which appears in the Current Report of Form 8-K/A of Mallinckrodt Inc. dated March 4, 1998. PRICE WATERHOUSE LLP San Francisco, California March 4, 1998