Wellbore integrity problem induced by insufficient seal ability of the cement sheath has become a technical challenge of shale gas wells during hydraulic fracturing. In this paper, a new model has been established to characteristic the mechanics of the casing-cement interface (CCI) and the cement-formation interface (CFI) of the shale gas wells. In this model, the radial stress and the stress intensity factor has been analyzed to predict the prolongation of the initial cracks caused by perforation through comparison of the stress intensity factor and the interfacial fracture toughness of the CCI and CFI. In addition, the influence of the casing and cement parameters on the interfacial stress and the crack width of the CCI and CFI has been discussed in detail, and the optimal design of these parameters has been proposed according to the field data. Finally, the conclusions and some realistic suggestions have been put forward based on the discussion.