A handpiece (1) is described for making holes in bone tissue including a surgical tool (3; 103) provided with a tip or head (40; 140) able to make a hole in the bone. The handpiece works by ultrasound, the tip (40; 140) of the tool includes a plurality of cutting elements (43) defining the profile of the hole to be made in the bone, and in the body of the tool there is provided a main channel (36) which ends in an outlet hole (44) opening in the tip of the tool (40; 140) for the passage of a cooling fluid, so as to cool the work area affected by the tool tip.