The invention relates to a tyre having a load index no lower than 118, made up of at least two layers (2, 6) of reinforcing elements. The first layer (2) is folded back around the bead wires and the second layer (6) extends from one bead to the other, the ends thereof being axially external to the most axially external of each of the bead wires. According to the invention, each of the carcass reinforcement layers (2, 6) has a breaking strength per unit of width of more than 2900 daN/dm, the minimum rigidity per unit of width, measured for an elongation of less than 10 %, of the second carcass reinforcement layer being strictly greater than a value equal to 20 % of the minimum rigidity per unit of width, measured for an elongation of less than 10 %, of the first carcass reinforcement layer, the reinforcing elements of the first carcass reinforcement layer having a yarn count of more than 300 tex, the reinforcing elements of the two carcass reinforcement layers having a yarn count of less than 750 tex, the elongation of the reinforcement layers of the second carcass reinforcement layer being greater than 8% under a force of 20 daN, and the secant modulus of elasticity under tension at 10 % elongation Mt, Mj comply with the relation Mt/Mj > 1.