Abstract: Based on the fact that the process of development of an earthquake is usually accompanied by fault creeps, a new mechanical model——the local internal stress modelfor tectonic earthquakes is proposed here by means of the mathematical theory of crack dislocation. It emphasizes the effect of the local internal stress caused by fault creeps in the process of development of an earthquake when the regional stress field is kept essencially constant. Change of internal stress with time and a two-dimensional quasi-static stress field thus given rise and the dimensions of the plastic zone beyond the tip of the crack are derived. The time and space characteristics of the premonitory anomalies before the occurrence of strong earthquakes are discussed.