In this study, Fatigue Crack Initiation of Socket Welds on Main Steam Line Small Bore Pipe in Nuclear Power Plant were derived through ASME Code, Sec.III and Sec.VIII. Fatigue Crack Initiation was assessed by taking and not taking Mean Stress from welding residual stress into account, with an evalutation of Equilibrium Equivalent Structural Stress. These are presented ASME Nuclear Facility Components Code, Sec.III and ASME B&PV Code, Sec.VIII, Div, 2. As a result, it was assessed that The Equilibrium Equivalent Structural Stress is the most effective option.