A reamer for chip removing machining includes a holder having a line of pockets, each pocket including a support surface facing in a direction of feed of the holder. Cutting inserts are mounted in respective ones of the pockets and project out of the pocket at progressively greater distances. Clamping assemblies clamp respective inserts in their respective pockets. Each clamping assembly includes a shank projecting into a hole formed in the pocket, a clamping head fixed to the shank and situated in the pocket, and a spring yieldably biasing the shank and the clamping head to a position wherein the clamping head forces a rear surface of the insert against the support surface. By depressing a shank against its spring bias, a respective insert can be replaced.