A piping system including straight pipes, elbows and tee branches in a nuclear power plant is mostly subjected to severe loading conditions with high temperature and pressure. In particular, the wall-thinning of an elbow due to flow accelerated corrosion is one of safety issues in the nuclear industry. In this respect, it is necessary to investigate the limit loads of an elbow with a wall-thinned part for evaluating integrity. In this paper, three dimensional plastic limit analyses are performed to obtain limit loads of an elbow with different bend angles as well as defect geometries under internal pressure and in-plane/out-of-plane bending moment. The limit loads are also compared with the results from limit load solutions of an uninjured elbow based on the von Mises yield criteria. Finally, the effects of significant factors, bend angle and defect shape, are quantified to estimate the exact load carrying capacity of an elbow during operation.