The invention relates to a device for clamping cutting inserts in recesses of cutter supports comprising a cam rotatably mounted in the cutter support and a clamping member provided on the cutter support. The clamping member is adapted to be pressed by the cam against the cutting insert and is designed as a pin secured in the cutter support in a cantilever manner. The free end of the pin is adapted to be displaced by the cam towards the cutting insert. In order to improve the run-off of cuttings, a clamping plate engaging the cutting insert is provided on the free end of the pin.