One bumper system for a vehicle includes a bumper bracket and a deformation element connected to the bumper bracket. The bumper bracket is composed of a metallic workpiece with an undulating form such that the bumper bracket has at least one undulation trough and at least two undulation peaks, and reinforcement zones are formed in regions of the undulation trough. Another bumper system for a vehicle includes a bumper bracket and a deformation element connected to the bumper bracket. The bumper bracket has an undulating form such that the bumper bracket has a plurality of undulation troughs and a plurality of undulation peaks, and reinforcement zones are formed in each undulation trough. In each system, a second deformation element may be connected to the bumper bracket, and at least one characteristic of the reinforcement zones may increase or decrease between the deformation elements and a middle of the bumper bracket.