The anchoring of the carcass reinforcing elements 1 is assured by circumferential cables 2, with the interposition of a connecting rubber composition 3. The circumferential cable 2 is arranged in several turns forming one or more helices. These circumferential cables have an operational elongation rate A.sub.f =A.sub.e +A.sub.p of more than 4%. This operational elongation rate does not include the specific elongation A.sub.s of the "cable" effect. The maximum stress R.sub.m of the cable 2 is preferably more than 2000 MPa. The cables have undergone a heat treatment which has, in combination, the features of being a recovery annealing treatment and which is carried out directly on cable comprising wires previously separately covered by an adherent coating.