A motor vehicle bumper consisting of an approximately U-shaped relatively elastic base body, of an apron made of elastic plastic material which covers the forwardly disposed web of the base body and is drawn around up to the flanges adjoining the web on both sides, and of a cover constructed as decorative strip and covering at least the remaining visible part of the upwardly disposed flange; the cover is thereby pivotally connected with the base body exclusively by fastening elements disposed substantially in the axial direction of the two bumper supports while the upper flange is surrounded at the end face by clamps formed out of the cover within the area of the bumper supports and possibly also within areas displaced outwardly with respect thereto.