A mold member for use in manufacturing a closed-torus tire comprises an annular inflatable resilient member having a substantially cylindrical inner wall and a corrugated outer wall opposed thereto. At the beginning of a tire manufacturing process, the mold member is expanded from its corrugated shape into a perfect toroid. A layer of rubber is first wrapped around the toroid and then a filament or cord is wound about the rubber. Upon the completion of the winding operation, additional rubber material is molded in a toroidal shape about the filament or cord so that the cord is fully embedded in rubber. Simultaneously with the molding operation, the additional rubber material is cast to a central wheel member. After vulcanization, the mold member is deflated from the expanded toroidal shape to the original corrugated form and the mold member is retained in the tire as a run-flat component, the corrugations forming a bumpy riding surface to inform a driver that a flat has occurred.