A tire having a radial carcass reinforcement comprising a crown reinforcement formed of at least two working crown layers of inextensible reinforcement elements, which are crossed from one ply to the other, forming angles of between 10° and 45° with the circumferential direction, which itself is topped radially by a tread, said tread being joined to two beads by means of two sidewalls. The tire comprises additionally at least in each shoulder a layer of reinforcement elements which are oriented circumferentially and have an undulation, the axially inner end of said additional layer being radially adjacent to the edge of a working crown layer, the axially outer end of said additional layer being located at a distance from the equatorial plane of the tire which is at least equal to the distance between said plane and the end of the working layer to which it is adjacent and the distance between said layer and the end of the axially widest working crown layer being greater than 1.5 mm.