Motor vehicle bumper with energy absorbing elements, and motor vehicle equipped with such a bumper

The bumper has a cross beam (3) with two lateral sections (9) fixed to respective rails (11). Supports (7) support absorbers (5) that are fixed to the beam for absorbing shock. The beam has housing (22) with a cavity (21) between a front face (15) and a back face (17) of the beam. Each support is a U-shaped clamp arranged on the beam for defining a box with walls of the housing for receiving the absorbers. An independent claim is also included for a motor vehicle.