Abstract: An energy absorbing bumper for attachment to vehicles, such as automobiles, is disclosed. The energy absorbing bumper includes a low density foamed plastic having a semi-rigid cellular structure, so that upon impact greater than a pre-determined minimum impact the energy absorbing material collapses, and absorbs substantially the entire impact, without any increase in its density. In particular, low density foamed plastics, such as urethane, are empolyed, having a density of less than 7 pounds per cubic foot. The bumper disclosed includes means for permitting collapse of the foamed plastic without any substantial increase in its density, so that the plastic itself absorbs substantially the entire force of impact upon the bumper.