A tire having a radial carcass reinforcement, comprised of at least one layer of metal reinforcing elements, said tire comprising a crown reinforcement, which is itself covered radially with a tread, said tread being joined to two beads via two sidewalls, wherein the metal reinforcing elements of at least one layer of the at least one layer of metal reinforcing elements comprising the carcass reinforcement are non-hooped cords having a permeability test flow rate of less than 20 cm3/min, wherein at least one layer of the at least one layer of metal non-hooped carcass cords is provided on at least one entire side with textile threads having air draining properties, the textile threads being oriented along a main direction parallel to that of the metal non-hooped carcass cords and wherein said textile threads are corrugated about this main direction.