This work deals with the computational modeling of Friction Stir Welding (FSW) processes including the discretization of the tools. The mechanical problem has been solved using a Stokes viscoplastic flow model with a suitable constitutive law for the range of deformation rates induced in the process. The thermal problem has been solved using an advection-diffusion model using an ALE formulation. Finite element formulations have been implemented for both problems. Two-dimensional and three-dimensional FSW problems have been solved under a number of particular process conditions and a particular tool geometry. Results obtained for the material flow around the tool have been compared with published experimental results, obtained under the same process conditions. A good correlation has been obtained between the numerical and the experimental results. The patterns of the material flow reported in the references, which were obtained using experimental techniques with tracers, have been identified performing the post-process of the results obtained for the material flow using computational visualization techniques with tracers. The role played by those visualization techniques in the analysis of the material flow around the tool, leading to a better understanding of the phenomena involved in the FSW process, is pointed out.