1. A pneumatic tire for vehicle wheels comprising a reinforced tread having a given width and side edges and two sidewalls made of elastomeric material, extending from said tread side edges and terminating in beads for a rigid wheel rim, said given width of the tread being wider than any other part of the tire and being reinforced over substantially the whole of its width by an annular structure which is substantially inextensible under the tire inflation pressure in both its circumferential and lateral directions, said annular structure extending to at least the midline of said sidewalls, said sidewalls having a cross-sectional shape whose midline, over substantially the whole length between said edges of the tread reinforcement and the bead, is convex with respect to the interior of the tire under the tire inflation pressure, each of said sidewalls having in combination a bending stiffness, curvature and thickness sufficient to constrain the sidewall between said side edges of the inextensible tread reinforcement and the bead seat on the wheel rim, whereby on inflation of the tire and under service conditions the sidewalls are placed under compression stress, said sidewalls having at least one end zone with a bending stiffness lower than the stiffness of the remaining zone, wherein at least on one of the surfaces of one sidewall grooves are present, whose direction forms an angle not greater than 45* with the radial planes of the tire, the pitch and the size of said grooves defining a plurality of ribs along which propagate the stresses exerted on said sidewalls.