A bumper for the front or rear section of a motor vehicle includes a cross member having a shell of U shaped cross section so as to define two legs interconnected by a crosspiece, and a mounting plate joined to the shell. The mounting plate has a U shaped configuration to define a longitudinal wall and two flanged portions which extend from the wall in a direction of the shell so that passageways are formed between the legs of the shell and the flanged portions of the mounting plate. A buffer is disposed anteriorly of the cross member and constructed for a snap fit to the mounting plate, with the buffer having spring legs for acceptance in the passageways.