A crash box for placement between a bumper beam and a side rail of a motor vehicle includes a longitudinal profile made of two U-shaped shells having overlapping ends sized to realize a material doubling for increasing side stiffness and to suit the side stiffness to a load level. A flange plate is provided on a side-rail-proximal end of the longitudinal profile and has an opening for passage of the longitudinal profile. The side-rail-proximal end of the longitudinal profile is configured with a collar which is turned outwards. The collar rests against the flange plate and is joined with the flange plate. In the event of a collision, the longitudinal profile of the crash box is moved into the side rail as the longitudinal profile folds into the side rail starting from the flange plate, while the side-rail-proximal end of the longitudinal profile remains secured to the flange plate.