When plastic deformation occurs in the piping under extreme seismic excitation, large damping effect will cause with the energy dissipation by plastic deformation. In this study, the simplified analysis method to obtain maximum response displacement of elastic plastic response of piping was investigated. The vibration energy and the dissipation energy with plastic deformation of piping were obtained by FEM analysis. The equivalent damping ratio depending on the piping response was formulated from both energies. On the other hand, piping response depends on the damping ratio. Both of them depending on each other were calculated as a pair of the converged values on each excitation level. The maximum displacements of the elastic plastic response calculated by this method resulted in appropriate simulation results to compare with excitation tests.