The invention provides a motor vehicle bumper comprising: a shield presenting a first impact zone situated substantially at the same height as the knee of an adult pedestrian and, immediately below said first zone, a second impact zone situated substantially at the height as the tibia of an adult pedestrian; a beam placed behind the shield substantially at the same height as the knee of an adult pedestrian, in register with and at a certain distance from the shield; and interposed between the beam and the shield, at least one block made of a compressible material, the block having a front end disposed beside the shield and a rear end disposed beside the beam, and having a cross-section that increases from its front end towards its rear end. The front end of the block is disposed in register with the second impact zone of the shield.