Abstract: By the strain analysis and energy method, the expressions of the axial stress and circumferential stress of an elbow under the action of an in-plane bending moment are gained, and the high order stress solution for an elbow subjected to an in-plane bending moment is suggested. The high order stress solution for an elbow subjected to an in-plane bending moment is compared with the solution using the other methods. It is obtained from the comparison that the high order solution is more accurate and is suitable for elbows without the limit of λ. The high order stress solution is suitable for an elbow under an in-plane close-bending moment or an in-plane open-bending moment.