The heavy road vehicle radial tyre with H/S form ratio not more than 0.60, with a top bracing ply (2) consisting of at least two cross fibre working laps (21, 22) and of at least one circumferential cord lap (20), arranged above the body ply (1) and a tyre tread (10) of length L. It is characterised in that between the circumferential cord lap (20) and the first radially innermost working lap (21) is set a layer of a rubbery mixture (4) with low modulus of elasticity, of constant thickness between 2 and 3 mm and having a width LM equal to L21, while the second radially external working lap (22) of axial width L22, greater than width L21, is radially separated from the edge of the circumferential cord lap (20), by a rubber pad (5) of high modulus of elasticity, axially extending from the end of the working lap (21) beyond the end of the circumferential cord lap (20), and, radially external to said pad (5),by a rubber wedge (6) with a modulus intermediate between the low and the high moduli and axially extending substantially from the edge of the radially external working lap (22) to a point axially internal to the end of the working lap (21).