The use of magnesium alloys is rapidly increasing in automotive and aerospace industries. Accurate constitutive modelling of material at high temperature is a key input for numerical simulation of manufacturing processes. In the present work, hot tensile deformation behaviour of AZ31 alloy was studied by performing uniaxial tensile tests in the temperature range of 250°C–450°C and strain rates ranging from 0.1  to 0.001 s−1. The flow stress behaviour of AZ31 alloy was modelled using two rate-dependent inelastic models, viz. Garafalo law and extended Ludwik law. Various constants in these models were predicted as a function of strain rate and temperature. These rate dependent laws were integrated using Finite Element (FE) based algorithms for thermo-mechanical simulation. Evolution of thermal stresses in solid state quenching and static casting of AZ31 alloys were studied. Results reveal that both material models accurately predict the evolution of thermal stresses for high temperature quenching and casting processes.