We developed numerical models to efficiently simulate the low-cycle fatigue behavior of a pipe elbow. To verify the model, in-plane cyclic bending tests of pipe elbow specimens were conducted, and a through crack occurred in the vicinity of the crown. Numerical models based on the erosion method and tie-break method are developed, and the numerical results are compared with experimental results. The calculated results of both models are in good agreement with experimental results, and the model using the tie-break method possesses two times faster calculation speed. Therefore, the numerical model based on the tiebreak method would be beneficial to evaluate the strength of piping systems under seismic loadings. (C) 2018 Korean Nuclear Society, Published by Elsevier Korea LLC.