Bumper for a vehicle

Bumper, especially a rear bumper, for a motor vehicle comprises a transverse bumper support (1) consisting of a polygonal closed profile of uniform cross-section supported at its ends on the vehicle construction via rigid holding elements. The transverse support has at least one rigid support element (8) in a central longitudinal plane of the vehicle. The regions of the transverse support adjacent to the support element are deformable or collapsible. Preferred Features: The support element consists of an extruded profile. The transverse support has a profile consisting of a rectangular first profile part (T1) protruding from the vehicle construction and an adjoining trapezoidal second profile part (T2). Opposite-lying walls of the profile parts are curved.