Abstract: A toric membrane of reinforced rubber, used as a support for the tread of a tubeless tire and forming with the tire P and its mounting rim a rolling assembly, characterized in that, when inflated to a pressure p0 greater than the pressure p1 of the cavity of the tire, it has in the inflated state a crown radius RM less than the loaded radius RE of the tire when used at its recommended pressure, the membrane being reinforced in its crown by a crown reinforcement and a hooping reinforcement composed of circumferentially oriented cords or cables, and in its sidewalls by at least one reinforcement ply, wound around an annular reinforcement element having a breaking load slightly greater than that of the hooping reinforcement.