Film/substrate structure is a basic structure widely used in microelectronic and materials science and technology. The residual stress in the film induced by mechanical and thermal mismatch in the manufacture is an important cause of initialization and extension of interface crack. The modified three-parameter (Gamma(0),sigma/sigma(y),t) cohesive model was used to investigate the cleavage fracture under plastic atmosphere, the stress distribution in crack tip, the shape and physiognomy of crack tip and the influence of the parameter on fracture process. The model was also used to discuss the whole process of the initialization and extension of interface crack between uniform and functional graded metal thin film and ceramic substrate under residual stresses. This model was also used to analyze the interfacial crack extension between enhanced functional graded thin film and substrate. The results were compared with that of the uniform films. The characteristic of the interfacial crack in graded film/substrate was emphasized.