Base on equal pressure method, isothermal compression tests of AZ31 magnesium alloy at different strain rates of 0.005-5 s?1 and different deformation temperatures of 473-673K were performed by using Gleeble-1500 simulator. The in?uences of deformation temperature and strain rate on the ?ow stress and critical fracture strain were investigated, and established the basic model of critical fracture strain of AZ31. And then the predicted edge cracking model of hot rolling for AZ31 was obtained based on the basic principles of magnesium alloy rolling edge cracking and fracture criterion of Cockcroft Latham, which contains the material deformation activation energy and the technology parameters of rolling. In order to verify the correctness of the predicted edge cracking model was established ,the corresponding relationship was obtained between damage value and edge crack depth along the width direction by the finite element simulation and rolling experiments in the same conditions. The results showed that the average error was 11.3% between predicted values and measured values .