The purpose of this work is the modeling and simulation of the material behavior of aluminum alloys during extrusion processes. In particular, attention is focused here on aluminum alloys of the 6000 series (Al-Mg-Si) and 7000 series (Al-Zn-Mg). The material behavior of these alloys during extrusion is governed mainly by dynamic recovery and static recrystallization during cooling. The current material model is based on the role of energy stored in the material during deformation, as it acts as the driving force for microstructural development. The concept of internal variables is used to describe state quantities such as dislocation density, average grain size and average grain orientation. The focus of the current paper is on some of the numerical aspects of the extrusion process simulation such as contact problems and adaptive mesh refinement which should be considered in order to obtain more accurate and robust results.