A twistable closed profile crossmember for a rear axle of a motor vehicle, the crossmember making it possible to connect two longitudinal arms of the axle. The crossmember includes a tube including: end portions that are each connectable to one of the two arms; an intermediate portion that is deep-drawn so as to obtain a U- or V-shaped transverse section wherein the inner walls of the tube are separated by a space; and two transition portions having a transverse section modified to connect each end portion to the intermediate portion. The crossmember further includes two inserts, each closing one end of the intermediate portion on all or part of the length of each transition portion to avoid all contact between the inner walls at the intermediate portion when the crosspiece is subject to a twisting force.