A support device for a pneumatic tired wheel for supporting the tire in a deflated or run-flat condition includes circular segment support members, each having a transverse cylindrical web and opposed radially inwardly projecting flange portions. The support member segments are interconnected by linkages which provide for radially extending and retracting the segments so that the support device may be mounted on a fixed or one-piece wheel having a rim portion with a diameter less than the opposed tire bead support flanges and with or without removing a tire entirely from the wheel. Threaded bolts are mounted on the wheel rim and extend radially outwardly into engagement with a link member of each of the linkages to cause the linkages to radially extend or retract the support segments. The segment webs are crowned to aid in centering the tire on the support device during operation thereof and tire gripping surfaces may be formed on the segment webs to minimize lateral or circumferential slippage of the tire relative to the support device.