Abstract: A bumper for motor vehicles has a rigid support and a covering made of elastic material. The elastic material is provided with at least two arms extending from an edge of the covering that is adjacent the body in use. A first of these arms is located within the outside contour of the covering and includes a fastening section for attaching the material to the motor vehicle body, and a second of the arms forms an extension of the outside contour of the covering and conceals the first of the arms. A flexible hinge-like construction is utilized to connect the covering to the body, according to preferred embodiments, and so as to protect the body of the vehicle from deformation due to impact loading of the bumper.