The invention relates to a radial tire (1) for a heavy vehicle, in which, on either side of the equatorial plane, a hyperelastic reinforcement ply (323), which is arranged radially outwards of the working layers, covers the axial end of the working layer with the smaller axial width (322), the axial ends of which are at a minimum axial distance (Ds/2) from said end, containing hyperelastic cords (50). Said cords comprise filamentary elements (54) on a single layer (52). The distance between the center of each filamentary element (54) of the layer (52) and the main axis (A) of the cord is equal to half of the helix diameter Dh and is substantially constant and equal for all the metal filamentary elements (54) of the layer (52), the metal filamentary elements (54) defining an internal arch (58) of the cord, having the diameter Dv. Each metal filamentary element (54) has a diameter Df and a helix radius of curvature Rf, such that: 9 ≤ Rf / Df ≤ 30, and 1.30 ≤ Dv / Df ≤ 4.5. Said hyperelastic cords are embedded in a rubber compound.
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