This paper presents a steady-state simulation of friction stir welding based on a prior computational method developed in [Bastier, A., Maitournam, M.H., Dang Van, K., Roger, F., 2006. Steady state thermomechanical modelling of friction stir welding. Sci. Technol. Weld. Joining 11 (3), 278–288]. This simulation includes 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 and the temperature field during the process. In the second step, a steady-state algorithm based on an elastoviscoplastic constitutive law is used to estimate the residual state induced by the process. The steady-state assumption and the original elastoviscoplastic constitutive law are two key features of the present model. This calculation takes into account the whole thermal, metallurgical and mechanical history of the material since the algorithm is based on an integration along the path lines of the particles. The material considered is a 7050 aluminium alloy. It is observed that the longitudinal residual stress field has a two peaks profile: these two peaks are situated in the zone of high gradient of dissolved precipitates fraction. Finally, a parametric study about the influence of welding and rotational speeds is carried out. This parametric study shows that the higher the welding speed and the lower the rotational speed, the lower the temperatures and the lower residual distortions.