Reinforcing annular structure of radial tires

A vehicle tire comprising a radial carcass having a crown point on a meridian plane, a tread, an annular reinforcing structure between the carcass and tread, said annular reinforcing structure comprising at least two reinforcing layers of metal monofilaments, each monofilament being embedded in said reinforcing layers as a single individual, metallic element spaced from the adjacent filaments, said monofilaments of each layer being parallel to one another and inclined at an angle between 10.degree. and 30.degree. with respect to the direction of the equatorial plane of the tire, the monofilaments of one layer crossing those of the adjacent layer, said carcass having a radius of curvature on the meridian plane in its crown point of at least 400 mm.