Abstract A new flexural-slip structural restoration technique for three-dimensional (3-D) digital models has been developed. This technique utilises a slip method that preserves volume in 3-D, line length in a given unfolding direction (of a specified surface and of layers parallel to this surface), and orthogonal bed thickness. These constraints enable the restoration of 3-D fault-propagation, fault-bend and detachment folds. The 3-D model is comprised of objects such as interpreted horizon and/or fault surfaces that are created from irregular, triangulated meshes. For a given model, a parallel sinuous-slip system is calculated from the geometry of a specified template surface and from a fixed pin surface that passes through all vertices of the triangulated meshes in the specified folding direction. The entire slip system then is folded to a new shape, which is defined by a geometric surface that can be curved or planar. In doing so, all vertices within the system are transformed to their new locations to generate a newly-folded 3-D model. We demonstrate the 3-D restoration technique by using a case study of an evaporite-cored contractional fold in the NW German Basin. Our restorations depict the 3-D sequential growth of the fold from 146 Ma through late Mesozoic time, and show that the shortening direction was towards NNE with the main contractional phase initiating during the late Cretaceous.