The present invention provides a tire/wheel assembly and a run-flat support member. The tire/wheel assembly is formed as follows: a pneumatic tire is fitted to a wheel rim; and 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 wheel rim. In the tire/wheel assembly, a plurality of through-holes or wavy asperities are made in the inner rim of each of the leg portions of the circular shell along a shell circumferential direction. The inner rims in which these through-holes or asperities are formed are embedded in the elastic rings.