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. The metal reinforcing elements of at least one layer of the carcass reinforcement are non-hooped cords having, in the permeability test, a flow rate of less than 20 cm3/min and at least one layer of the carcass reinforcement being provided on at least one side with textile threads oriented mainly along a direction parallel to that of the metal reinforcing elements of said at least one carcass reinforcement layer, said textile threads being corrugated about this main direction.