A bumper (B), comprising an elongated hat-shaped cross beam (1) mounted to at least two crash boxes (2) which are attached to a vehicle, said cross beam (1) having a primary contact face in the form of bent longitudinal upper and lower flanges (3,4). The bent longitudinal upper and lower flanges being arranged in the direction of the cross beam (1), and said primary contact face is facing away from the vehicle. Said bent longitudinal upper and lower flanges (3,4) have each a portion (5) with a large inner radius (R) at least at the mounting site of the cross beam (1) to respective crash box (2) compared to a small inner radius (r) of the rest of each of the bent longitudinal upper and lower flanges (3,4).