With interdisciplinary cooperation in the fields of forming technology, mechanics, and numerical analysis within the SPP 1146, the fundamentals for an efficient analysis of the thermomechanical interaction between the forming tool and workpiece in incremental forming processes have been established. The main topics are processes with an approximate cyclic loading history and minimal tool cost like flow forming, ring rolling, incremental sheet metal forming or laser and plasma beam forming.For these processes, mathematical fundamentals and new modelling techniques have been developed and experimentally verified in the following categories: - technological studies, - material and contact mechanics analysis - and numerical methods studies. These methods are optimised for fast and detailed computation of the process.