Abstract: Earthquake is a kind of complex vibratory process. At present, oscillatory system is generally regarded as an elastic body in dynamic analytic methods,so its results can not well been shown when buildings failure in the course of earthquake, such as suddenly jumping and hysteresis effect.Its essential reason is that it neglects the nonlinear characteristics of structures.To consider the nonlinear oscillatory features, an improved dynamic analytic model is presented , and it is studied deepgoingly with catastrophe theory. Some useful conclusions are drawn.