Fatigue life prediction of pressure vessel is studied analytically using cumulative damage models and linear elastic fracture mechanics method. The stresses are analyzed by finite element method. During operation, the maximum stress occurs at the outside of neck region while fatigue analysis indicates that the bottom of nozzle part has the shortest fatigue life. Previously proposed fatigue life prediction equation and cumulative damage model are modified successfully by introducing reference fatigue modulus. It is found that the modified life prediction equation and damage model are useful for lower stress level application.