In this work, the numerical simulation of the FSW process is tackled by means of an Arbitrary-Lagrangian-Eulerian (ALE) formulation. The computational domain is split into three different zones: the work-piece (defined by a rigid visco-plastic behaviour in the Eulerian framework), the pin (within the Lagrangian framework) and finally the stir-zone (ALE formulation). A fully coupled thermo-mechanical analysis is performed accounting for the heat flux generated by the plastic dissipation in the stir-zone (Sheppard-Wright and Norton-Hoff rigid-visco-plastic constitutive models) as well as the frictional dissipation at the contact interface (Norton’s frictional contact model). The highly non-linear stress field typically encountered in FSW processes is worked out by means of a novel FE technology based on a three-field, velocity/dev(stresses)/pressure), mixed formulation. The result is an enhanced stress field approximation which enables for stress-accurate results in non-linear computational mechanics. The use of an independent nodal variable for the pressure field allows for an ad-hoc treatment of the incompressibility constraint. This is a mandatory requirement due to the isochoric nature of the visco-plastic strains in FSW processes. Finally, tracers have been implemented to show the material flow around the pin allowing a better understanding of the welding mechanism. The result is an accurate and robust methodology to study the FSW problem allowing for a clear visualization of the material behaviour at the stir-zone leading to a better understanding of the welding process itself. The results obtained from the proposed numerical simulation strategy are compared with the experimental evidence.