This work is concerned with numerical analyses of the forming behavior of magnesium at elevated temperature. For that purpose, a thermodynamically consistent, rate-dependent, finite-strain elasto-plastic constitutive model is presented. This model captures the stress differential effect as well as the anisotropy of magnesium. Furthermore, the change in shape of the yield locus (distortional hardening) is also taken into account. This constitutive law, together with its parameter calibration based on uni-axial tensile tests, is finally combined with the localization criterion originally proposed by Marciniak and Kuczynski and applied to the simulation of forming limit test. Comparisons to experiments show the excellent predictive capabilities of the model.