A run-flat tire 1 comprises a carcass 6, a pair of side reinforcing rubber layers 9, and a pair of sidewall rubber components 10. At a tire maximum-width position, a first side reinforcing rubber layer 9A disposed in the side of a first bead portion has a thickness B1 greater than a thickness B2 of a second side reinforcing rubber layer disposed in the side of a second bead portion, and a first sidewall rubber component disposed in the side of the first bead portion has a thickness A1 smaller than a thickness A2 of a second sidewall rubber component disposed in the side of the second bead portion.

A tire comprises, in the central part of its crown, at least one undulation (51) of the radially outermost crown layer, having a radial amplitude A at least equal to 1 mm. At least one bead comprises, aside from the radial carcass layer and the bead wire, a radial reinforcing element that is such that the axial distance between the radial reinforcing element and the axially innermost carcass layer is at least equal to 1 mm and at most equal to 12 mm at the point of the radial reinforcing element that is situated 30 mm from the radially innermost point of the bead wire, for a better trade-off between the stiffness of the undulating crown and of the bead.