The deformation behavior of AZ31 magnesium alloy has been investigated by isothermal compression at temperatures between 573-723K and at constant strain rates ranging from 10-3 -1s-1. It is shown that the form of flow stress curves is very sensitive to temperature and strain rate. In the experimental domain studied, the flow stresses are modeled using a power law with an average activation energy of 145.16 kJ/mol, and dynamic recrystallization (DRX) occurs. The critical strain for DRX is determined by analysis of flow stress curves. The ratio of the critical strain to the peak strain falls in the range of 0.4-0.5. At low temperatures and high strai rates, the deformation become macroscopically inhomogeneous, and the fracture of the specimens is accompanied by shear banding. Grain refinement resulting from DRX is less effective at high temperatures due to rapid grain growth. It is also shown that there is no difference between peak stress and stable state stress at high temperatures and lower strain rates, presenting the feature of continuous dynamic recrystallization (CDRX).