Disclosed are a run-flat tire and a tire/wheel assembly in which the workability of the tire-to-rim fit has been improved while including a core-type run-flat support member. The tire/wheel assembly is formed by coupling a pneumatic tire and a rim of a wheel. In the tire/wheel assembly, the run-flat support member constituted of a circular shell and elastic rings is inserted into a cavity of the pneumatic tire, in which the circular shell has a support surface thereof extended toward the periphery of the tire and leg portions along each side of the support surface, and the elastic rings support the leg portions of the circular shell on the rim. At the same time, a seat portion and an engaging portion are provided for at least one of the elastic rings, in which the leg portion of the circular shell can be settled on the seat portion, and the engaging portion is extended in an outer tire axial direction from the seat portion and sandwiched between a tire bead base and a rim seat.