The invention relates to a bumper (1) for a motor vehicle, particularly a front bumper, comprising at least two deformation elements (2) which are spaced apart from one another and whose central or longitudinal axes are aligned, when mounted, substantially parallel to the direction of travel of said motor vehicle, as well as a plurality of cross-members (3.1, 3.2, 3.3, 3.4) which have a closed profile and are arranged one above the other and connected to said deformation elements (2). In order for the bumper to provide relatively high resistance at a low weight such that in the event of a collision at speeds lower than 20 km/h, rearward displacement of the cross-member is limited in a targeted manner and movement of the bumper (1) upwards or downwards caused by the bumper of the other vehicle implicated in the collision is prohibited, said cross-members (3.1, 3.2, 3.3, 3.4) are formed from a group of at least three cross-members, each of these cross-members (3.1, 3.2, 3.3, 3.4) of the group having an at least five-cornered cross-sectional profile.