A round formwork module comprising a flexible skin having a front side which, when used, constitutes the forming surface for a concrete structure which is to be cast, and also provided with a rear side and a supporting structure which is arranged on the rear side of the skin and which can be displaced in order to enable the skin to be bent along a direction in which it extends. The invention is characterized in that the supporting structure has a base structure and two side elements which are arranged laterally, close to the base structure. The side elements are respectively secured to a lateral edge area of the skin and protrude therefrom close to the base structure. An adjustment device for adjusting the curvature is provided in between the base structure and the side elements.