A run flat tire wheel assembly having a flat run support formed by a ring-shaped metal shell and rubbery elastic members in a tire rim cavity, said tire wheel assembly improving bondability between the ring-shaped metal shell and rubbery elastic members by making said rubbery elastic member from a rubber composition including 100 parts by weight of a diene-based rubber, 40 to 90 parts by weight of carbon black, 3 to 8 parts by weight of sulfur, 0.1 to 1 part by weight of an organic acid cobalt salt in terms of content of cobalt element, 0.1 to 3 parts by weight of a phenylene-diamine-based antiaging agent, and 1 to 6 parts by weight of a resol-type alkylphenol resin.