The present invention provides a tire/wheel assembly and a run-flat core, which enable reduction of a cavity resonance generated in a case where the run-flat core is inserted into a cavity formed between the pneumatic tire and a rim of a wheel. In the tire/wheel assembly of the present invention, the run-flat core is inserted into a cavity formed between the pneumatic tire and the rim of the wheel, the run-flat core includes a pair of elastic rings which are disposed on the rim respectively along bead portions of the pneumatic tire, and a circular shell which stretches between the elastic rings and extends in the tire circumferential direction. A sound absorbing member is provided to the circular shell.