A reinforced rubber toric membrane, inflated to a pressure p0 greater than the pressure p1 of the cavity of the tire in which it is used, having, in the inflated state, a crown radius RM less than the loaded radius RE of the inflated tire, and being, in its crown, reinforced by at least two plies of cords or cables crossed from one ply to the next, at least one of the plies being a hooping ply of cords or cables, oriented circumferentially, and reinforced in each of its sidewalls by at least one reinforcement ply, wound around an annular reinforcement element, and formed of reinforcement elements, each being composed of a core having a breaking load which is firstly greater than the tension, per element of ply, due to the pressure differential p0-p1 and to the maximum centrifugal force to which said element is subjected, and secondly such that it permits the breaking of said reinforcement elements for a pressure differential p0-pnull1 greater than p0p1 and after the breaking of the elements of the hooping ply, around which core is wound at least one cord or cable, the elongation at break nullR of the reinforcement element being at least equal to the ratio of the difference between the internal meridian length of the tire and the external meridian length of the membrane to the external meridian length of the membrane.