A bumper beam for mounting to a frame assembly of a motor vehicle at one end of the motor vehicle includes opposing end portions adapted to be mounted to the frame assembly of the motor vehicle and a centrally disposed intermediate portion extending between the end portions. The end portions and the intermediate portion define an upper wall, a lower wall, and a central wall between the upper and lower walls. The upper and lower walls each have an elongated arcuate flange that extends from a free end of a respective upper and lower wall along a length of the bumper beam. The arcuate flange of each of the upper and lower walls defines an outwardly facing concave surface and an inwardly facing convex surface.