A support member curved about an axis of revolution for mounting on a wheel rim inside a tire chamber to support the tire in a deflated condition. The support member has a generally U-shaped cross section and may have open ends or the ends may be closed with webs having edges joining the radially inner and outer peripheral edges of the support member.A relatively lightweight high-strength material such as reinforced plastic may be used in the construction of the support member with relatively long fibers of reinforcing material extending generally in planes containing the axis of revolution and relatively short fibers of reinforcing material extending generally circumferentially of the support member and in planes perpendicular to the axis of revolution. Heat-conducting material in the form of wire screen or short lengths of wire may be embedded in the support member to conduct heat away from the surface engaged by a deflated tire.