Tire with radial carcass with outside to inside turn-ups

A tire having an aspect ratio of less than 0.8 and having a radial carcass reinforcement (1) surmounted radially by a crown reinforcement, the carcass reinforcement (1) being formed of at least one ply of cords or cables and being wound in each bead (B) around an anchoring bead ring (2), going from the outside to the inside in order to form a turn-up (10), characterized by the fact that the said turn-up (10) is located to the inside of an angle .alpha., open axially toward the inside and radially toward the outside, of at most 45.degree. and defined by two straight lines OD.sub.1 and OD.sub.2 tangent to the circle circumscribed round the anchoring bead ring (2), the straight line closest to the axis of rotation of the tire being parallel to said axis.