The energy wave scattering method (EWS method) makes use of transmission lines and junctions to model the systems, and switches physical quantities to be energy wave variables then simulates the dynamic response of the systems, finally switches the analyzed results from energy wave variables back to physical quantities. Although using EWS method to simulate the dynamic response of structures is still on the initial stage, figuring out the time domain problems as example as transient analysis is suitable for use. Transient analysis is an important segment of dynamic analysis, it needs more extensive mathematics and newer method of calculation. Probably the EWS method is a workable and typical way. The study tries to use the EWS method to simulate the dynamic response of mutildegree of freedom systems, the response are due to different factors such as initial condition factors, damping factors and external force factors else. Let the simulated results display as displacement-time figures and displacement tables, and compared the results from lumped method or the finite element software-ANSYS with system characteristics by the figures and time domain displacements by the tables. On the whole, the simulated results almost matched with the analytical lumped methods. From the results of the study could confirm the feasibility that using the EWS method to simulate the dynamic response of mutildegree of freedom systems, and further tested and verified the applications of the EWS method on the dynamic analysis.