The carcass reinforcement of a radial tire having a substantially cylindrical tread reinforcement meets the tread reinforcement tangentially at points of the tread reinforcement near or at the edges thereof, and the carcass and tread reinforcements are substantially in contact with each other over a width at least equal to the minimum width of the carcass reinforcement at the height of the bead wires. This permits continuous high-speed travel without danger of ply separation.