Stress analysis has been performed using computer program ANSYS in the pressurizer surge line in accordance with ASME Sec. III in order to predict possibility of fatigue failure due to thermal stratification phenomena in pipes connected to reactor coolant system of nuclear power plants. Highly vulnerable area to crack generation has been chosen by the analysis of fatigue due to thermal stress in pressurizer surge line. This kind of result can be helpful to choose the location requiring intensive care during inservice inspection of nuclear power plants.