The invention relates to a bumper for a motor vehicle, in particular a front bumper, having at least two deformation bodies which are at a distance from one another and of which the center or longitudinal axes, in the mounted state, are oriented substantially parallel to the direction of travel of the motor vehicle, and having a plurality of crossmembers which have a closed profile and which are arranged one above the other and are connected to the deformation bodies. The crossmembers are formed from a group of at least three crossmembers, wherein the respective crossmember of the group has a cross-sectional profile which comprises at least five corners.