A bumper for a motor vehicle with a support part which, supports and separates an impact-near and an impact-remote layer of energy-absorbing form. The supporting part is held by resilient holders on a support fixed to the vehicle. A panelling covers the impact-near layer towards the front and is fixed to the support part. A skirt adjoins toward the bottom. In order to increase the absorbency and retain a pedestrain-protective configuration, the support part is designed as a stiff load distributing support and the panelling is fastened to it and merges integrally with the skirt.