We have developed a simplified analysis method based on equivalent linearizations for calculating inelastic seismic responses of piping systems. The linearizations of inelastic load-deformation relationships make it possible to take advantage of a conventional method for elastic seismic design, such as modeling using elastic beam elements and the modal response spectrum analysis. To linearize the stiffness equivalently, we modified the flexibility factors of the elastic beam elements used in a conventional design. As a result, we can apply the conventional design code in the developed method. By doing so, we found that the calculated seismic responses of a simple piping system agree fairly well with those from nonlinear time-history analysis. This agreement verifies that the simplified analysis method can efficiently evaluate inelastic responses.