Abstract: A motor vehicle bumper for energy absorption. A support part of the bumper is supportable on the vehicle and is generally U-shaped with horizontally extending arms. A cover supported on the support includes respective wall sections that extend in from the top and bottom of the cover and cooperate with vertically outwardly extending flanges on the legs of the U. The wall sections of the cover are simply locked to the flanges of the support. A body of energy absorbing material is disposed in the cover and in the support and is pressed against the wall sections of the cover upon deformation of the cover by application of more than a predetermined force to press the energy absorbing material against the cover wall sections to prevent those wall sections from separating from the flanges of the legs of the U-shaped support in the event of collision or application of more than a predetermined force to the cover of the bumper.