A tool for chip removing machining, including a primary tool part and a secondary tool part. The primary tool part includes a primary connecting surface, an opposite surface, a recess that extends from the primary connecting surface toward the opposite surface, and a wall section between a bottom surface of the recess and the opposite surface. The secondary tool part includes a secondary connecting surface, a protuberance that extends from the secondary connecting surface and, in a mounted state, into the recess, the protuberance having an end surface that, in the mounted state, faces the bottom surface of the recess. A shaft part is for fixing in a machine tool. A fastening element, which, by a contractive force in the mounted state, connects the wall section with the protuberance. A center axis extends in a longitudinal direction of the tool through the primary tool part, the recess, the secondary tool part, the protuberance, and the shaft part. An insert seat is formed in at least one of the primary tool part and the secondary tool part for receiving a cutting insert. The wall section is elastically flexible and, in the mounted state, bent toward the end surface of the protuberance by the contractive force of the fastening element.