A run-flat support body for run-flat vehicle wheels. The support body is typically embodied as a shell-shaped, metallic annular body having an undulated supporting annular surface. A simple, effective method for producing one such annular body, according to which a rectangular blank which is cut out of a strip of sheet metal is bent along the longitudinal side to form a ring and the open ends of the ring are interconnected by a material connection. The annular blank thus produced is provided with the desired profile according to the pressure-rolling method, is provided with connecting elements, and cut open between the same.