In large plant facilities, elbow and straight pipe have large potion in whole piping system. When the cracks are initiated in pipe, the cracks have to be evaluated using fracture mechanics parameter such as J-integral. Unlike calculating J-integral of straight pipes, estimation J-integral of elbow using finite element analysis is not easy. Because the effect of geometries for crack behavior of elbow are more complex than straight pipes. Also, there is another difference between elbow and straight pipe. That is unequal thickness in intrados and extrados. Unequal thickness of elbow pipes generally occurs by the manufacturing process. Thickness in intrados is getting thicker than nominal thickness but thickness in extrados is getting thinner than nominal thickness. So first, this paper provides a reference stress-based J-integral estimation of circumferential through-wall cracked elbow with equal thickness. And this paper provides also a reference stress-based J-integral estimation of circumferential through-wall cracked elbow with unequal thickness. To find the reference stress-based approximate J-integral, various ratio of thickness (t), pipe radius (r), pipe bend radius (R) and crack length (θ) are considered. And three-dimensional finite element analyses using elastic property for elastic crack behavior and elastic-perfectly plastic property for limit load are performed. Finally Results in this research are presented in the failure assessment diagram (FAD) space.