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 .