A comparative study was carried out on AZ31 (Mg-3Al-1Zn) magnesium alloy to understand the effect of deformation mode on the hot flow stress. Accordingly, the peak flow stress resulted from hot compression, hot tension, and hot torsion tests were correlated to the Zener-Hollomon parameter using the Sellars-McTegart approach. Based on the analysis, by applying the lattice self-diffusion activation energy of magnesium (135 kJ/mol) as the deformation activation energy, the hyperbolic sine exponents were determined to be ~ 5. Consequently, by consideration of creep exponent of 5, some reliable semi-empirical constitutive equations were proposed for high-temperature deformation of AZ31 alloy and the effect of deformation mode was quantified.