The influence of stress state on the high temperature workability of rolled AZ31 Mg alloy was investigated on the basis of a processing map. To construct the processing map, high temperature compression tests were carried out on samples oriented parallel to the rolling direction at various temperatures (25°C~450°C) and strain rates (10, and then the results were compared with those of a torsion test. The overall efficiency profiles of both the compression and torsion processing maps were similar to each other, but the index of dissipation efficiency in the torsion was somewhat lower than that in the compression. The microstructure of the compressed specimens revealed much finer grained structure than that of the torsion specimens. Such microstructural differences were attributed to the different tendencies of twin formation and texture evolution depending on the stress state.