A bumper arrangement includes a cross member and two deformation elements for arrangement between end regions of the cross member and longitudinal members of a motor vehicle. The cross member is hollow with a front and rear walls and upper and lower walls. The front wall has a depression extending in longitudinal direction of the cross member. The depression has a deepest region extending at a distance from the rear wall. The upper and lower walls of the cross member each have in the end regions a further depression which extends in longitudinal direction of the cross member, so that the upper wall and the lower wall are more corrugated in the end regions than in a central region of the cross member, so that the distance between the front wall and the rear wall in the end regions is smaller than in a central region of the cross member.