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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 temperatures and strain rates for magnesium alloy AZ31. To calculate the thermal mechanical stresses, the thermal flow of twin-roll casting process was simulated firstly; then the stresses were calculated by the imposed thermal flow as the body load, and a small displacement load along roller’s tangential direction was imposed simultaneously in order to simulate the rolling action. The stresses and deformation results were compared with experimental data. Based on the stresses analysis and experimental tests, it reveals that separating force should be strictly controlled in the twin roll casting process in order to avoid cracks caused by thermal and deformation stresses.