A bumper with an attachment member to be made thereon for the purpose of mounting the bumper onto longitudinal beams of a vehicle, is such that section walls acting as compressive and tensile struts and a pair of flanking walls joining them form a hollow section. The attachment member is in the form of a hollow section exhibiting at least one side wall and two transverse walls following on therefrom with a length of hollow section with the longitudinal beam. The hollow section is in the form of a push-fit length matching the inner cross-section of the longitudinal beam. The other end region of the attachment member is provided with collar-type parts projecting from their end edges and aligned approximately parallel to the transverse walls. In a use position, the collar-type parts of the attachment member are aligned with the flanking walls of the bumper and are releasably attached to it. The bumper is bolted to the collar-type parts of the attachment member.