The present investigation aims at studying and modelling the flow behaviour of the AZ31 magnesium alloy by means of torsion tests performed in extended ranges of temperature and strain rates. Two types of rheological models were considered. The former is based on the power law equation, whilst the latter is based on the Sellars and Tegart approach. The effectiveness of the two constitutive models in describing the flow behaviour of the AZ31 magnesium alloy under investigation was evaluated. It was observed that both the equations are able to predict the flow behaviour of the material at different temperatures and strain rates. In particular, the former is very effective in predicting the hardening stage of the flow curve, whilst the latter allows to fit the softening stage. The models were used for the finite element analysis of a complex extrusion process and the results, in terms of the load-stroke curves, compared to each other.