Manufacturing processes based on cutting have been extensively automated over the past 30–40 years leading to greatly increased flexibility of operation. In contrast, processes based on ductile forming have largely remained dependent on fixed tooling and lack flexibility. Recent innovations have shown that forming can also be made flexible, by new process configurations typically using simpler and smaller tools with increased (and controllable) freedom of motion. In order to facilitate development of such flexible forming processes, this paper examines the possibility that all such processes can be predicted and organized so that subsequent process development may be based on selection rather than invention. The approach taken is based on Zwicky’s “morphological analysis,” in which the features of a design are parameterized and an exhaustive search is conducted, with appropriate constraints used to reject infeasible designs. As an example of this approach, the process of ring rolling is explored, and a “periodic table” of 102 “elemental” ring rolling machines is presented. The combination of elements into compounds is described, and the use of the table for development of practical flexible machines is discussed. Having applied this approach to the example of ring rolling, its likely value in exploring other processes is discussed.