The ASME B & PV Code Sec. allows the socket weld for the nuclear piping in spite of the weakness on the weld integrity. Recently, the integrity of the socket weld is regarded as a safety concern in nuclear power plants because many failures and leaks have been reported in the socket weld. OPDE (OECD Piping Failure Data Exchange) database lists 108 socket weld failures among 2,399 nuclear piping failure cases during 1970 to 2001. Eleven failures in the socket weld were also reported in Korean NPPs. Many failure cases showed that the root cause of the failure is the fatigue and the gap requirement for the socket weld given in ASME Code was not satisfied. The purpose of this paper is to evaluate the fatigue crack behavior of a surface crack in the socket weld under fatigue loading condition considering the gap effect. Three-dimensional finite element analysis was performed to estimate the fatigue crack behavior of the surface crack. Three types of loading conditions such as the deflection due to vibration, the pressure transient ranging from P=0 to 15.51MPa, and the thermal transient ranging from T=25oC to 288oC were considered. The results are as follows; 1) The socket weld is susceptible to the vibration where the vibration levels exceed the requirement in the ASME Operation and Maintenance (OM) Code. 2) The effect of pressure or Temperature transient load on the socket weld integrity is not significant. 3) No-gap condition gives very high possibility of the crack initiation at the socket weld under vibration loading condition. 4) For the specific systems having the vibration condition to exceed the requirement in the ASME Code OM and/or the transient loading condition from P=0 and T=25oC to P=15.51MPa and T=288oC, radiographic examination to examine the gap during the construction stage is recommended.