Bumper system for narrow mounting space

The bumper system has two deformation elements each fixed to a longitudinal support, and a cross member (1) with a U-profile is fastened to the deformation elements. A half shell extends from the longitudinal support to a rear side of the U-profile, and another half shell extends from the longitudinal support over the cross piece (2) of the U-profile to a front side of the cross member, and the deformation elements are fastened on the U-profile by a front locking plate.