A bumper for a motor-vehicle having a box-shaped cross-section, comprising an elongated bumper member made of plastics material and having an open cross-section substantially shaped like a "C", said bumper member being closed in the rear by one removable reinforcing wall comprising a substantially rectilinear lamina having at each end one enlargement radiused to the plane of the lamina by means of a slanting plane and provided with transversal holes for a stable anchoring of the reinforcing wall to the bumper member and to the motor-vehicle, said reinforcing wall having along its longitudinal borders first coupling means which are engageable with corresponding second coupling means provided along the opposite longitudinal borders of the bumper member, said first and second coupling means providing a solid joining of the bumper member and reinforcing wall.