A tool for machining has a main body, a seat formed on the main body, a fastening screw, and a cutting insert. The seat has a base surface for supporting an underside of the cutting insert and a lateral bearing surface. A bore for receiving the fastening screw is formed in the base surface, the bore has a threaded bore portion and, closer toward the base surface, a thread-free bore portion. The cutting insert is fastened to the seat such that the head portion of the fastening screw is supported on the through-hole in the cutting insert. The threaded portion of the fastening screw engages with the threaded bore and the fastening screw is elastically deflected such that a thread-free shank portion bears against the thread-free bore portion on a side remote from the lateral bearing surface and is spaced apart from the thread-free bore portion.