A bumper beam for a vehicle has two attachment portions (15, 16) with a U-shaped cross section open towards the vehicle. Each attachment portion has a reinforcing member (29) in the form of a hat-profile located within the attachment portion and across the latter, with its webs (31, 32) welded to the webs (13, 14) of the attachment portion. The side flanges (33, 34) of the hat profile have holes (35, 36) for bolts by means of which the side flanges and thereby the bumper beam can be attached to a structural part of the vehicle and the attachment section has holes (41) to allow fastening bolts of this kind to be fastened through these holes.