Abstract: Currently, analytical methods based on seismic energy of structures mainly focused on the simplified estimation approach of input energy and hysteretic energy. As a result, the response of structures can’t reflect the effect of time-frequency characteristics of earthquake energy. A mathematical model is proposed in this paper to reflect the time varying characteristic of momentary input energy. By establishing the relationship between the time varying characteristic of momentary input energy and the deformation history of a linear single degree of freedom (SDOF) system, the paper developed a simplified procedure to simulate the deformation history, which was validated using the maximum deformation and cyclic demand spectrum of a linear system. It is found that the simulated deformation response can reflect the max amplitude of actual deformation and the effect of duration. This research provided theoretical foundation for the study on the simulated deformation history and the quantization of cumulative damage.