Motor vehicle bumper and motor vehicle

The invention relates to a motor vehicle bumper having a internal bumper part which can be fastened to a motor vehicle body, and a external bumper part fastened at least section-wise to the internal bumper part. The invention relates also to a motor vehicle with a bumper according to the invention. A motor vehicle bumper has an internal bumper part mountable on a motor vehicle body. An external bumper part is fastened to the internal bumper part. The internal bumper part includes a base body fastened to the motor vehicle body and a holding bar fastened by a releasable fastener to the base body. An edge of the external bumper part is releasably fastened thereto. The holding bar is unfastened from the base body by the application of force to the external bumper part on the lengthwise direction of a motor vehicle and to the vehicle body.