Considering the strain weakness behavior of fault and the visco-elasticity of surrounding rocks . A simple mechanical model for fault earthquake is put forward . First

the equivalency between the model and cusp catastrophe is proven . Then

the cusp catastrophe theory is applied to analyse the instability mechanism of the fault earthquake. It is explicated that the quick transferring of energy and the violent releasing of energy dont takeplace unless the enough energy from external world is input into the mechanical system and the stiffness ratio is less than unit . The period of seismogeny is both related to the period of loading owing to distant field displacement and to the visco-elasticity behavior of surrounding rocks.