Bumper assembly for motor vehicle

The assembly (10) has a cross-piece (12) extended to a transverse axis (Y) of a car, and shock absorbers (14, 16) transversely spaced from each other and connected to the cross-piece, where each absorber is interposed between the cross-piece and a longeron. Each absorber has a central core (44) to connect the cross-piece to the longeron and a shell (46) deformed by an effect of longitudinal compressive force. The shell surrounds the core and includes a lower half-shell (98) and an upper half-shell (100). The cross-piece and the absorbers are made of composite material.