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 and the axially widest working crown layer being radially internal to the other working crown layers. The tire additionally comprises in each shoulder at least one layer of reinforcement elements which are parallel to each other in the layer and are oriented radially relative to the reinforcement elements of the working layer radially adjacent to said additional layer, the axially inner end of said additional layer being radially adjacent to the edge of the radially outer working crown layer, and at least part of said additional layer being radially and/or axially adjacent to the edge of the axially widest working crown layer, the ratio of the elasticity modulus of a layer P to the elasticity modulus of the calendering layer of the working layer adjacent to the additional layer being of between 0.5 and 1, said layer P being arranged between at least part of the working crown layers, the axially outer end of said layer P being axially between the ends of the axially least wide and widest working crown layers.