Abstract: A bumper construction for vehicles includes an elongated high-strength metal beam roll-formed from sheet steel, and at least one structural molded piece made of polymeric material attached to opposing end sections of the beam. Each structural piece has a rearwardly swept front surface that forms aerodynamically stylized corners at the ends of the beam. Each structural piece further provides attachment structure for attaching the beam to a vehicle, with the attachment structure being configured to transmit front impact forces compressively through the structural pieces to the vehicle frame, while minimizing the torsional and tensile forces on the attachment structure. The structural pieces further include a recess for closely receiving and supporting an impact-resisting flange on the beam to stabilize the beam during impact. The mateable engagement simplifies assembly, and further provides for high-energy absorption upon front impact of a vehicle.