The invention relates to an assembly comprising a vehicle bumper skin and a channel-section bumper impact absorber, the absorber being made of thermoplastic material and comprising a web and two flanges, each having a free longitudinal edge and an opposite longitudinal edge that is connected to the web, the flanges and the web defining a longitudinal channel, in which the bumper skin and absorber are connected together in such a manner that the concave side of the absorber faces towards the bumper skin.