Twin-roll thin strip casting process combines casting and hot rolling process into a single step; in which melt and solid states exist in the casting region, so its deformation is more complex than rolling process. In this paper, Anand’s model, a unified visco-plasticity constitutive model, was employed to simulate the highly nonlinear behavior in the twin-roll casting process. Anand model’s parameters were regressed based on compression tests at various temperature and strain rate for magnesium alloy AZ31. To calculate the thermal mechanical stresses, the thermal flow of twin-roll casting process was simulated firstly; then stresses were calculate, in which the temperature field result of thermal flow was imposed as body load, and a small displacement load along roller tangential direction was imposed simultaneously in order to simulate rolling action. The deformation results can well describe the forward slip zone, backward slip zone and melt eddy zone in the casting region. Based on the results, the applicability of Anand’s model on twin-roll casting process was discussed.