Annular tire overlay (11) for drawing onto the rolling surface of tires (40), which has a tread (17) on its outside and a gripping surface (15) on its inside, which tire overlay (11) is so designed that contact between the rolling surface of the tire (40) and the surfacing of the road is prevented by the tire overlay (11) when the tire overlay has been drawn onto a tire. The said tire overlay (11) is provided with a flange (21) which stops the tire overlay (11) from shifting in the axial direction of the wheel. Advantageously, the tire overlay is additionally stiffened by a flange (21) of planar form to keep the contact area on the surface below small.