Abstract: Safety tire comprising a tread (11) reinforced by an inextensible belt (23), spaced beads (12), and side walls (14) connecting the beads to the sides of the tread, defining below the latter a central inflatable chamber (15), each side wall at least being reinforced by a carcass (21), and comprising on the inside of the carcass a supporting shaped part or support member (20) of lenticular section, made of an elastomer and extending from the vicinity of the beads (12) to below the edges of the belt, said tire being characterized in that the said shaped supporting parts (20) are constituted by two parts with different flexibility, whereof one (20.sub.1) disposed near the inner face of the carcass (21) is of a more flexible elastomer while the other (20.sub.2) disposed inside the tire is of less flexible elastomer.