Bumper for motor vehicle

Between a back of a first impact part (32) facing the vehicle boot (12) and the vehicle boot itself is a cross support attachment (40) which is connected through assembly spots (34) to the vehicle body (10). An interspace is provided in the longitudinal direction of the vehicle between the back of the first part and the front of the cross support and the impact element (32) is provided with such elastic energy break down capacity that when the impact speed of the vehicle is below 5 km/h against a fixed barrier there is only an elastic deformation of the impact element so that the back of the first part reaches maximum the front of the cross support attachment.