Abstract: The hot deformation behavior of AZ31 magnesium alloy was investigated by thermo-compression tests with Gleeble-1500D thermal simulator.The tests were performed in the temperature range from 473 to 723 K and at strain rates from 0.001 to 1 s-1.The steady flow stress was described by the hyperbolic sine constitutive equation.The processing maps were drawn and analyzed according to the dynamic material model.The results show that the instability zones of flow behavior could also be recognized by the maps.The optimal processing parameters of hot deformation under the test condition was able to be attained by the maps as follow: hot deformation temperature of 473-523 K and strain rate around 0.01 s-1.The superplastic forming could be performed when the temperature was 623-673 K and strain rate was about 0.001-0.006 s-1.The range of strain rate could be wider when the deformation temperature was higher than 673 K.