A bumper beam has a generally U shape with a central flange (12; 12′) and two webs (13, 14; 13′, 14′), which central flange in the longitudinal middle portion of the beam points outwards from a vehicle and has a longitudinal concavity (17; 17′), which deepens progressively towards the end portions of the beam in order to change to or connect to fastening plates (20, 21; 20′, 21′).