A phase-field model is modified to investigate the grain growth and texture evolution in AZ31 magnesium alloy during stressing at elevated temperatures. The order parameters are defined to represent a physical variable of grain orientation in terms of three angles in spatial coordinates so that the grain volume of different order parameters can be used to indicate the texture of the alloy. The stiffness tensors for different grains are different because of elastic anisotropy of the magnesium lattice. The tensor is defined by transforming the standard stiffness tensor according to the angle between the(0001) plane of a grain and the direction of applied stress. Therefore, different grains contribute to different amounts of work under applied stress. The simulation results are well-explained by using the limited experimental data available, and the texture results are in good agreement with the experimental observations. The simulation results reveal that the applied stress strongly influences AZ31 alloy grain growth and that the grain-growth rate increases with the applied stress increasing,particularly when the stress is less than 400 MPa. A parameter(?d) is introduced to characterize the degree of grain-size variation due to abnormal grain growth; the ?d increases with applied stress increasing and becomes considerably large only when the stress is greater than 800 MPa. Moreover, the applied stress also results in an intensive texture of the 0001 axis parallel to the direction of compressive stress in AZ31 alloy after growing at elevated temperatures, only when the applied stress is greater than 500 MPa. A phase-field model is modified to investigate the grain growth and texture evolution in AZ31 magnesium alloy during stressing at elevated temperatures. The order parameters are defined to represent a physical variable of grain orientation in terms of three angles in spatial coordinates so that the grain volume of different order parameters can be used to indicate the texture of the alloy. The tensor for different grains are different because of elastic anisotropy of the magnesium lattice. The tensor is defined by transforming the standard stiffness tensor according to the angle between the ( 0001) plane of a grain and the direction of applied stress. Thus, different grains contribute to different amounts of work under applied stress. The simulation results are well-explained by using the limited experimental data available, and the texture results are in good agreement with the experimental observations. The simulation results reveal that the applied stress strongly infl uences AZ31 alloy grain growth and that the grain-growth rate increases with the applied stress increasing, particularly when the stress is less than 400 MPa. A parameter (? d) is introduced to characterize the degree of grain-size variation due to abnormal grain growth; the? d increases with applied stress increasing and gain substantial large only when the stress is greater than 800 MPa. Moreover, the applied stress also results in an intensive texture of the 0001 axis parallel to the direction of compressive stress in AZ31 alloy after growing at elevated temperatures, only when the applied stress is greater than 500 MPa.