The process of flow forming is numerically modeled using finite element codes based on the Forge2005® software. Two numerical approaches are considered. The first one uses an updated Lagrangian formulation. The problem is solved with help of a self-contact management algorithm. The second approach consists in using an ALE formulation that permits to optimize meshing with an adaptive method based on the Zienkiewicz-Zhu error estimation. The ALE method is well adapted to incremental forming processes such as flow forming and allows dealing with difficulties generated by the contact between the work piece and tools. Both formulations are coupled with complex tool kinematics. The Lagrangian formulation gives realistic results. The ALE formulation is promising with regard to computational time, and simulations on simple configurations show fairly good agreements with Lagrangian results. © 2007 American Institute of Physics.