A segmental annular tire safety support for mounting on a wheel rim to support a pneumatic tire in the deflated condition. The safety support includes a segmental curved member having a generally cylindrical radially outer supporting surface of revolution with a substantially constant radius circumferentially of the tire safety support. The ends of the curved member have radially outer end surfaces which are relatively flat and are spaced from the axis of the support a distance less than the length of the radius of the outer supporting surface of the curved member to reduce the stresses generated at the end edges and to provide warning vibrations and noise during operation of the tire in the deflated condition.