The simulation of hot extrusion processes is a difficult and challenging problem in process modeling. This is due to very large deformations, high strain rates and large temperature changes during the process. Computer models that with sufficient accuracy can describe the material behavior during extrusion can be very useful in process and product development. Today, the process development in industrial extrusion is to a great extent based on trial and error and often involves full size experiments. Numerical simulations can most likely replace many of these experiments, which are often both expensive and time consuming. The motivation for this research project is a request for accurate finite element models that can be used in process design and development of stainless steel tube extrusion. The models will be used to investigate the effect of different process parameters on the quality of the extruded tube. In the work presented in this thesis, thermo-mechanically coupled simulations of glass-lubricated tube extrusion were performed. Extrusion models in two and three dimensions were developed. Only extrusion problems with radial symmetry were considered. Simulations were carried out using the commercial code MSC.Marc, which is a Lagrangian finite element code. Frequent remeshing was therefore needed during the analyses. The models were validated by comparing predicted values of extrusion force and exit surface temperature with measurements from an industrial extrusion press. The two- dimensional model was shown to provide good and fast solutions to extrusion problems with radial symmetry. A two-dimensional model is sufficient for many applications and this model is planned to be used for solving process problems further on. For the three-dimensional model it was concluded that a very fine mesh would be needed to successfully predict the extrusion force using four-node tetrahedrons. This would result in unacceptably long computational times. The future work will be aiming at improving the three- dimensional model in order obtain accurate results within a reasonable time. To obtain reliable simulation results a good constitutive model is crucial. This work has focused on the use of physically based material models, which are based on the underlying physical processes that cause the deformation. It is expected that these models can be extrapolated to a wider range of strains, strain rates and temperatures than more commonly used empirical models, provided that the correct physical processes are described by the model and that no new phenomena occurs. Physically based models are of special interest for steel extrusion simulations since the process is carried out at higher strain rates than what are normally used in mechanical laboratory tests. A dislocation density-based material model for the AISI type 316L stainless steel was used in the finite element simulations included in this thesis. The material model was calibrated by data from compression tests performed at different temperatures and strain rates.