This paper describes examinations of the screening criteria of fracture assessment methods for pipes having a circumferential surface flaw. The failure mode screening criteria for ferritic steel pipes are defined in Appendix E-11 of the Rules on Fitness-for-service for Nuclear Power Plants [1] (hereinafter, the FFS Codes) of the Japan Society of Mechanical Engineers (JSME) and ARTICLE C-4000 of ASME Section XI [2] (hereinafter, ASME Sec. XI). However, these screening criteria were assessed under limited conditions; they are not intended for detailed evaluation. Essentially, the fracture mode depends on a stress-strain curve, a J-R curve, flaw shape (length and depth), pipe shape (R/t), etc. First, among these parameters, these that have a large effect on fracture strength evaluation were selected. The important parameters for fracture strength are a stress-strain curve, a J-R curve, flaw depth. Next, failure modes according to these parameters were classified. Finally, a screening method to determine whether the failure mode is Limit Load (LL) or Elastic-Plastic Fracture Mechanics (EPFM) for all pipe materials was proposed. The proposed method is a general method not limiting the applicable pipe materials.