Abstract: By combining the theory of continuum damage mechanics with initial stress and strain fields and criteria for element failure and crack initiation, a predictive model of crack initiation under creep-fatigue interaction was constructed. Based on the model, a user defined material subroutine (UMAT)was compiled and creep-fatigue damage accumulation was investigated by the finite element method using ABAQUS codes. Crack initiation was simulated in a structure without initial defects under a creep-fatigue interaction. Factors affecting the time of crack initiation were investigated. In contrast to linear cumulative damage (LCD) theory, mutually promoting effects exist between creep damage and fatigue damage at crack initiation locations. Interaction between creep and fatigue shortens the time to crack initiation. The sequence of creep and fatigue loading greatly influences accumulation of damage at the crack initiation location. Cyclic loads cause larger damage after long periods of creep load compared with periods without creep load, hence time to crack initiation is shorter.