In this study, the applicability of a previously developed optimal seismic design methodology, which can consider the structural integrity of not only piping systems but also elasto-plastic supporting devices, is studied for seismic waves with various frequency characteristics. This methodology employs a genetic algorithm and can search the optimal conditions such as the supporting location and the capacity and stiffness of the supporting devices. Here, a lead extrusion damper is treated as a typical elasto-plastic damper. Numerical simulations are performed using a simple piping system model. As a result, it is shown that the proposed optimal seismic design methodology is applicable to the seismic design of piping systems subjected to seismic waves with various frequency characteristics. The mechanism of optimization is also clarified.