A series of inelastic benchmark and parametric analyses was conducted on the tests of a pipe elbow and a piping system model made from carbon steel to investigate variabilities of elastic–plastic analysis results and clarify the factors affecting the analytical results. The analysis on the pipe elbow was the inelastic static analysis and the analysis on the piping system model included the inelastic dynamic analysis under the random input motion. From the benchmark analysis results, we found that setting the yield stress in the material property approximation had a significant influence on the inelastic analytical results, while the work hardening modulus in the bilinear approximation of the stress–strain curve had little influence. The parametric analysis was performed with the viewpoint to examine the influence of the yield stress and the work hardening modulus when the material property was approximated as the bilinear relation. The results also showed that the setting of the yield stress had larger impact on the analytical results than the setting of the work hardening modules. The parametric analysis results confirmed that the variation in the analytical results among different analysts would be reduced by using the same material property approximation.