A wheel assembly provides a mount for a pneumatic tire having two tire beads. The wheel assembly includes a disk defining a hub receiving center and an outer peripheral edge. The wheel assembly also includes a rim that is fixedly secured to the outer peripheral edge. The rim has first and second tire seat surfaces and a well separating the first and second tire seat surfaces. First and second rim flanges are secured to the first and second tire seat surfaces, respectively, such that each of the first and second rim flanges extend out from each of the first and second tire seat surfaces at an angle less than or equal to thirty degrees. The wheel assembly also includes anti-roll off devices that interact with the tire through the flat rim flanges of the wheel assembly. A run flat device, including an inner rim bonded to an inner tube, which is, in turn, bonded to an interior carcass surface of the tire. The run flat device maintains a round shape in the tire tread even if a foreign object, such as a nail, penetrates the tire and compromises the tire pressure thereof.