Abstract: In order to evaluate the engineering safety of pipe elbows, a mechanical model has set up to formulate the meridian stress of pipe elbows subjected to open-bending moments. The construction of the meridian-stress formula due to open-bending moments has the similar appearance with that due to close-bending moments. Except for the relation of tension stress and compress stress transforming each other on the same place, there are different values in meridian stress. The open-bending meridian stress is always larger than close-bending meridian stress for different bending moment coefficients and different angles on the cross section. But the formula-shape of open-bending circumferential stress looks identical with that of the close-bending one. Their stresses have equivalence and reverse relation. Under the action of an in-plane bending moment, elastic stress of pipe elbows just is a special case of the elastic stress of reducing elbows. The elastic stress of reducing elbows may be attained by replacing the cross-section radius of pipe elbows with that of the reducing elbows.