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Using a differential form of the potential energy function and taking the effect of work applied by external force in far field into account, the mechanism of strike-slip fault earthquake is analyzed. The research indicates that each characteristic displayed with a fold catastrophe model in the catastrophe theory corresponds to a specific primary characteristic of the strike-slip fault earthquake. The fold catastrophe can describe the positions of starting and end points of a fault failure and the distance of fault dislocation. These include the description of stability of the surrounding rock-fault system before and after the earthquake. Two different illustrations about elastic energy releasing amount of the surrounding rock with the fault failure are shown with the primary characteristics mutually demonstrated. The intensity of strike-slip fault earthquake is related to the surrounding rock press and the stiffness ratio of surrounding rock and fault. The larger the Surrounding rock press, the smaller the stiffness ratio. The larger the included angle between the tangential stress axis and the causative fault surface, the stronger the earth-quake.