Abstract: An elastomeric energy absorbing bumper mounting mechanism for a vehicle comprises an energy absorbing block formed of an elastomeric material, desirably a crystalline thermoplastic polyester material, formed into an intersecting grid of elastomeric walls, with a stiffer inboard side than outboard side, thickened peripheral end walls, triangular reinforcing cells, tapered cell walls, thickened posts at the intersections of certain walls, and a portion of partial length cells. The block is heat staked to rigid end plates at each end to form energy absorbing units, and the end plates are bolted to a bumper beam and vehicle rail plates. Two energy absorbing units support the bumper beam and are easily replaceable and adaptable to other vehicles.