A run-flat support and tire assembly designed so that when air sealed within a tire is lost, the vehicle may be supported by support members in place of air pressure within the tire. The run-flat tire has a split rim, a tubeless tire mounted on the rim, and a plurality of annularly disposed circular support members. The support members each comprises a thin-wall casing body having lattice-like reinforcing ribs for partitioning the interior of the casing body into a plurality of chambers. Connecting protrusions project from the casing body. The connecting protrusions are detachably connected to one another for each incorporation of the support members into the tire.