With MY (mean yield) criterion, the limit load of defect-free pipe elbow under inner pressure is analyzed, and an analytical solution is first obtained. The solution shows that the limit load is a function of wall thickness t, average radius r, yield strength as well as curvature radius R0. The limit load increases with the increase of the curvature radius R0 and will get the same value with the burst pressure of straight pipe if R0→∞. The limit load calculated by the solution is compared with those based on Tresca, Mises, as well as TSS yield criteria. It is also concluded that Tresca criterion predicts a lower bound to the limit load, while TSS criterion predicts an upper bound one. However, the limit load based on the MY criterion lies just between the TSS and Tresca solutions, most notably, the MY criterion almost has the same prediction precision with Mises solution.