An apparatus particularly suitable for countersinking rivet holes preformed at circumferential spacings in the fuselage (30) of an airplane and in annular reinforcing ribs (31) of H-shaped cross sectioon in the fuselage at axial spacings. The apparatus comprises a frame (41) wsith a toolhead (22) mounted thereto, and a carrier arm (1) cantilevered to the frame for insertion in the fuselage and reinforcing ribs. For making possible the speedily countersinking of two annular rows of rivet holes formed in those parts of the outer flange of each reinforcing rib (31) which are on the opposite sides of its web, a fluid motor (5) and a fluid-actuated cylinder (6) are supported on the distal end of the cantilevered carrier arm (1). The cylinder has a piston rod (6b) to which there is coupled an offset anvil assembly (15) for pressing the fuselage and a rib against the toolhead (22). the piston rod (6b), together with the anvil assembly (15) thereon, is not only linearly displaceable but also rotatable about its own axis. The fluid motor (5) is geared to the piston rod for revolving the anvil assembly through an angle of at le3ast 180 degrees.