Cutter head for accommodating multiple cutters, wherein the cutter head has a separate receptacle opening for each of the cutters, and wherein the cutter head includes clamping means for clamping the cutters in the receptacle openings. A cavity is implemented in the cutter head in the region of at least one of the receptacle openings, which is separated by a thin wall or layer from this receptacle opening, and the cavity can be filled with a fluid and a pressure can be applied thereto.