Tyre for a motor vehicle, comprising the following in a meridian plane: two beads intended to be mounted on a rim, two sidewall layers connected to the beads, and a crown having a tread, the crown having a first side connected to the radially outer end of one of the two sidewall layers and a second side connected to the radially outer end of the other one of the two sidewall layers; at least one carcass reinforcement extending from the two beads as far as the crown, the carcass reinforcement having a plurality of carcass reinforcing elements and being anchored in the two beads by way of a turn-up around a bead wire, so as to form a main part and a turn-up in each bead; in each bead, the bead wire having the form of a closed circumferential ring, bracing the bead of the tyre against the rim and comprising a first part made of a first material M1 taking the form of textile cords, said first part interacting with a second part of the bead wire made of a reinforcing second material M2, the bead wire having a circumferential bending stiffness defined as the product of the Young's modulus and the area moment of inertia of a meridian section through the bead wire in the circumferential direction, expressed in N.m 2 and measured according to the ISO 178 standard, characterized in that the tensile stiffness of the bead wire is comprised between 4.5x10 5 N/m and 1.8x10 6 N/m; the circumferential bending stiffness of the bead wire is greater than or equal to Kr * (1000*D / (16*25.4)) 3, where D is the diameter of the wheel on which the tyre is mounted, measured at the seat of the rim in metres, and where Kr is equal to 2.10 -2 N.m 2; the elastic elongation of the bead wire is greater than or equal to 2%. two beads intended to be mounted on a rim, two sidewall layers connected to the beads, and a crown having a tread, the crown having a first side connected to the radially outer end of one of the two sidewall layers and a second side connected to the radially outer end of the other one of the two sidewall layers; at least one carcass reinforcement extending from the two beads as far as the crown, the carcass reinforcement having a plurality of carcass reinforcing elements and being anchored in the two beads by way of a turn-up around a bead wire, so as to form a main part and a turn-up in each bead; in each bead, the bead wire having the form of a closed circumferential ring, bracing the bead of the tyre against the rim and comprising a first part made of a first material M1 taking the form of textile cords, said first part interacting with a second part of the bead wire made of a reinforcing second material M2, the bead wire having a circumferential bending stiffness defined as the product of the Young's modulus and the area moment of inertia of a meridian section through the bead wire in the circumferential direction, expressed in N.m 2 and measured according to the ISO 178 standard, the tensile stiffness of the bead wire is comprised between 4.5x10 5 N/m and 1.8x10 6 N/m; the circumferential bending stiffness of the bead wire is greater than or equal to Kr * (1000*D / (16*25.4)) 3, where D is the diameter of the wheel on which the tyre is mounted, measured at the seat of the rim in metres, and where Kr is equal to 2.10 -2 N.m 2; the elastic elongation of the bead wire is greater than or equal to 2%.