Elbows with various shapes of local wall thinning were numerically analyzed by finite element method to get load-displacement curves and the maximum loads. Results were compared with the experimental data obtained by another study. Elastic-plastic analysis were carried out under the combined loading conditions of internal pressure and in-plane bending loads. Two types of bending loads were considered such as elbow opening mode and elbow closing mode. Also, two different wall thinning geometries were modeled. Wall thinning area located extrados or intrados of elbow inner surface was considered. Longitudinal and circumferential lengths of the thinning area and the thinned thickness were varied for analysis. The results showed that the maximum load of the wall-thinned elbow decreased with increasing of the circumferential thinning length and the thinned thickness in both of extrados and intrados thinning locations in both loading types. The maximum load obtained by the analysis were in good agreement with the experimentally measured maximum load with the same wall thinning type and dimensions. This supports accuracy of the analysis results obtained in this study.