This paper provides method of an elasto-plastic analysis for practical seismic design of nuclear piping system. JSME started up the task to establish method of an elasto-plastic analysis for nuclear piping system. The benchmark analyses have been performed in the task to investigate on method of an elasto-plastic analysis. And our company has participated in the benchmark analyses. As a result, we have settled on the method which simulates the result of piping exciting test accurately. Therefore the recommended method of an elasto-plastic analysis is shown as follows; 1) An elasto-plastic analysis is composed of dynamic analysis of piping system modeled by using beam elements and static analysis of deformed elbow modeled by using shell elements. 2) Bi-linear is applied as an elasto-plastic property. Yield point is standardized yield point multiplied by 1.2 times, and second gradient is 1/100 young's modulus.Kinematic hardening is used as a hardening rule. 3) The fatigue life is evaluated on strain ranges obtained by elasto-plastic analysis, by using the rain flow method and the fatigue curve of previous studies.