A collision damping arrangement for absorbing energy in a possible head-on and/or rear end collision of a motor vehicle, having respectively a bumper-side cross member (1; 18) and longitudinal members (4, 5; 19) which are arranged on the cross member and which are also connected to the corresponding passenger compartment, with at least one collision damper (2, 3; 15, 16; 17) being arranged on a respective longitudinal member (4, 5; 19). In order to permit the collision damper (2, 3; 15, 16; 17) to be produced in a straightforward manner and at reasonable cost, and a precise matching of a predeterminable collision behavior of the vehicle in a simple manner, the collision damper (2, 3; 15, 16; 17) is comprised of an extruded section whose profile extends transversely to the longitudinal axis (6) of the longitudinal member (4, 5; 19) for the motor vehicle.