A radial ply tire comprises a tread, sidewall and bead regions. At least the region of severe flexing of the sidewall when the tire is run in a deflated or substantially under-inflated condition comprises a rubber compound which has a rebound resilience of at least 87 percent, and more preferably of at least 90 percent, measured by the Lupke pendulum method according to B.S. 903/1950 and a hardness in the range of 45 - 65 Shore A.