A tire comprising a crown, two sidewalls and two beads, a carcass reinforcement anchored in each of the beads and a crown reinforcement. The carcass reinforcement comprises at least two circumferential alignments of first reinforcing threads of high elasticity modulus, each circumferential alignment of the first reinforcing threads being, within each bead, bordered axially inwardly and axially outwardly by second reinforcing threads, oriented substantially circumferentially, of a modulus greater than or equal to that of the first reinforcing threads. The first reinforcing threads and second reinforcing threads are separated by a layer of mix of very high elasticity modulus. Considering ΣRI as being the total of the rigidities of extension of the second reinforcing threads arranged axially inwardly relative to the carcass reinforcement and considering ΣRE as being the total of the rigidities of extension of the second reinforcing threads arranged axially on either side of the carcass reinforcement, then: 0.6 ≤ Σ R I Σ R E ≤ 1.5