Bending stress at plastic collapse for a circumferentially cracked pipe is predicted by limit load equation provided by the Appendix C of the ASME Code Section XI. The equation of the Appendix C is applicable for pipes with both external and internal surface cracks. On the other hand, the authors have developed an equation taking into account the pipe mean radii at non-cracked area and at cracked ligament area. From the comparison of Appendix C equation and the new equation, the plastic collapse stress estimated by the Appendix C equation gives 20 to 30% less conservative bending capacity prediction for external cracked pipes with small Rm/t, where Rm is the pipe mean radius and t is the pipe wall thickness. This paper discusses the limitation of the use of Rm/t for the Appendix C equation.