Abstract Understanding the state of stress, strain and the temperature of an aluminium alloy going through a die during extrusion is of great importance for running the aluminium extrusion process, because they are closely related to the surface quality of the extruded products, throughput and scrap rate. It has been made clear that surface tearing is mainly caused by excessive local tensile stresses at the surface of the extrudate and hot shortness is due to the heat generated during the process that brings the extrudate temperature above the incipient melting point of the billet material. Both the state of stress and the temperature are complicatedly related to the extrusion conditions including initial billet temperature, ram speed, reduction ratio, friction at the interfaces, deformation resistance of the billet material, die geometry, as well as thermal characteristics of the billet material and the tooling. The practical means to accurately measure the stress, strain and temperature is yet quite limited. In the present work, 3D FEM simulation of the aluminium extrusion process was performed to determine the state of stress, strain and the temperature of a commercial aluminium alloy going through square and round dies. It has been found that at the same process conditions, the state of stress in the aluminium alloy going through a round die is more favourable than going through a square die, especially at a high reduction ratio. The magnitude of the tensile stress component at the corners of the square extrudate is much higher than at the surface of the round extrudate, which makes the square extrudate more tearing prone. Simulation also reveals that while temperature evolution during the process is similar for both of the die shapes, temperature rise across the section is prominent, especially at sharp corners of the square extrudate. This has been ascribed to the non-uniform metal flow through the square die.