<p>A pneumatic tire has a carcass ply (12) of cables of a high tensile material have stiffening members (21,22) of a textile material disposed on each side and adjacent to the turn-up portions (27) of the carcass ply. The textile cords in one stiffening member are oriented in an opposite manner from the cords of the other stiffening member with respect to a circumferential line of the tire.</p>