A bumper for a vehicle contains a bumper cross beam extending in a transversal direction of the vehicle, a bumper cover forming the external face of the bumper, and an energy-absorbing insert disposed at least in parallel between the mounted bumper cross beam and the bumper cover. The insert has a plurality of deformation cavities and/or deformation free spaces. The insert has a first boundary layer, a medial layer, and a second boundary layer. The medial layer has a different energy absorptive capacity than the two boundary layers and is associated with the bumper cross beam. The deformation cavities and/or deformation free spaces are embodied in the medial layer such that in case of a collision, the insert is plastically deformable at least partially in the transversal and/or longitudinal direction of the vehicle along a small part of a block length to absorb energy.