This paper presents a computational method for the simulation of a welding process called friction stir welding. This simulation is divided into two main steps. The first one uses an Eulerian description of the thermomechanical problem; a 3D mixed finite element model based on a computational fluid dynamics package is used to establish the material flow, the temperature and the pressure fields during the process. These results are compared with experimental data. The second step of the simulation is more original. A part of the initial geometry is extracted in order to evaluate the material flow in a local domain around the tool. A steady state algorithm is then used to calculate the residual state induced by the process. This calculation takes into account the whole mechanical history of the material because the algorithm is based on an integration along the trajectories of the particles. Finally, the residual stresses of a friction stir welded assembling are evaluated. It should be noted that only the steady state phase of the process is simulated, which leads to a substantial reduction of computational time.