A tire configured to be mounted on a mounting rim, comprising two beads, a crown comprising a tread, two sidewalls, a carcass reinforcing armature, and a membrane situated radially on the inside of the carcass reinforcing structure, this membrane comprising: (a) a membrane reinforcing armature anchored in each bead to the annular reinforcing structure, said membrane comprises a layer of reinforcement elements directed substantially radially and (b) an airtight layer of rubber mix; wherein the membrane is arranged in such a way that part of the membrane together with part of the carcass reinforcing armature delimits a chamber extending transversely and circumferentially; wherein, in any radial section, the curved length Lm of the trace of the surface of the chamber delimited by the membrane is greater than the curved length Lc of the trace of the surface chamber delimited by the carcass reinforcing armature (Lm>Lc).