A bumper system for vehicles includes a tubular beam having front, top, bottom, and rear walls, and further having open tubular ends. The bumper system further includes a pair of mounting brackets each having a V-shaped mounting section attached to the rear wall of the open tubular ends and having an integral corner-forming section extending from the mounting section laterally around the associated ends and forwardly to a location where the corner-forming section attaches to the front wall of the one end. The corner-forming section includes a resilient portion shaped to flex and absorb energy upon corner impact, and further is adapted to transfer energy directly to the vehicle frame, thus providing efficient and effective energy absorption upon corner impact.