A tire/wheel assembly comprising: a wheel having a disc and a rim provided on the outer peripheral edge of the disc in such a manner that the widthwise center of the rim is offset towards one side; a pneumatic tire mounted on the rim; and a run-flat support member disposed in the cavity of the pneumatic tire, the run-flat support member having an annular shell and elastic rings, the annular shell including a support surface located radially outwardly thereof and two leg portions formed radially inwardly thereof in a straddling state, the support surface having a plurality of convexly curved surface sections that are widthwisely arranged, the elastic rings supporting the leg portions on the rim. One of the elastic rings located on the opposite side of the rim to the offset side is smaller in rigidity than the other of the elastic rings located on the offset side.