The collapsible tire includes at least one carcass reinforcement that is surmounted radially from the outside by an inextensible crown reinforcement, which is radially on an inside of a tread. The reinforcements each include at least one layer of reinforcing elements. The tread is connected to two beads by two sidewalls. The beads are intended to come into contact with a rim, and each bead has at least one circumferential reinforcing element called a bead wire. The bead wire defines a mean line which forms a substantially circular closed curve in a circumferential plane. The bead wires are flexible and have at least one concave part Pc with a radius Rc and a center of curvature Cc.