The triaxial experiments of rock mechanics completed recently show that rock failure can be caused not only by increasing of maximum principal stress, but also by change(increasing or decreasing)of intermediate principal stress and by decreasing of minimum principal stress. Concerning that earthquakes are rock failure under triaxial stress state in the crust, it is pointed that earthquakes can be caused not only by increasing of maximum principal stress, but also by decreasing of intermediate principal stress or minimum principal stress. Before earthquakes there must be a process of increasing of stress or renergy, but earthquakes mustn't happen in the process of increasing of stress or energy. Earthquakes can happen in the process of decreasing of stress or energy. The action which can cause the stress decreasing in the crust was discussed, and the possibility of earthquakes caused by stress decreasing was searched by seismic activity.