Tyre for a heavy duty vehicle, the aspect ratio H/L of which is strictly greater than 0.75 and the inflation pressure P of which is greater than or equal to 6.5 bar, with a radial carcass reinforcement, comprising a crown reinforcement comprising two working crown layers (41, 42) of reinforcing elements which are crossed from one ply to the other, making with the circumferential direction angles (α1, α2) of between 8° and 45°, the said angles α1 and α2 being oriented one on each side of the circumferential direction, the crown reinforcement being capped radially by a tread, the said tread being connected to two beads via two sidewalls, characterized in that at most the said two working crown layers (41, 42) being the only ones present to form the crown reinforcement over at least 40% of the axial width of the crown reinforcement, in that the reinforcing elements of the radially outermost working layer form an angle α2 with the circumferential direction which is greater in terms of absolute value than the angle α1 formed by the reinforcing elements of the radially innermost working layer with the circumferential direction, in that the absolute value of the difference between the absolute values of the angles α2 and α1 is greater than 9°, and in that the mean angle α satisfies the relationship: 14 + 131 ∗ exp − L / 100 < α < 20 + 164 ∗ exp − L / 100, α being defined by the relationship Arctan((tan(|α1|) ∗ tan(|α2|)) 1/2), L being the maximum width of the tyre measured in the axial direction and expressed in mm, in that the rupture potential index F2/FR2 of the radially outermost working layer is less than1/6, in which: FR2 is the breaking force in uni-axial extension of the cords of the radially outermost working layer, F 2 = p 2 ∗ Tc ∗ tan α 1 / tan α 1 + tan α 2 / cos 2 α 2 + C, where Tc = 0.092 ∗ P ∗ Rs ∗ 1 − Rs 2 − R L 2 / 2 ∗ Rt ∗ Rs, C = 0.00035 ∗ min L − 80 / sin α 1, L − 80 / sin α 2, 480 − 480, p 2 is the pitch at which the reinforcing elements of the radially outermost working crown layer are laid, measured perpendicular to the reinforcing elements at the circumferential median, Rs = Re − Es, Re is the external radius of the tyre, measured at the radially outermost point on the tread surface of the tyre, the said surface being extrapolated in order to fill any voids there might be, Es is the radial distance between the radially outermost point of the tyre and the orthogonal projection thereof onto the radially exterior face of a reinforcing element of the radially innermost working crown layer, RL is the mean of the radii of the axially outermost points on each side of the tyre, Rt is the radius of the circle passing through three points situated on the exterior surface of the tread outside of the voids, defined from a shoulder end at respective axial distances equal to 1⁄4, 1⁄2 and 3⁄4 of the width of the tread. p 2 is the pitch at which the reinforcing elements of the radially outermost working crown layer are laid, measured perpendicular to the reinforcing elements at the circumferential median, Rs = Re − Es, Re is the external radius of the tyre, measured at the radially outermost point on the tread surface of the tyre, the said surface being extrapolated in order to fill any voids there might be, Es is the radial distance between the radially outermost point of the tyre and the orthogonal projection thereof onto the radially exterior face of a reinforcing element of the radially innermost working crown layer, RL is the mean of the radii of the axially outermost points on each side of the tyre, Rt is the radius of the circle passing through three points situated on the exterior surface of the tread outside of the voids, defined from a shoulder end at respective axial distances equal to 1⁄4, 1⁄2 and 3⁄4 of the width of the tread.