Abstract: In the numerical simulation of hydraulic fracturing in a shale gas reservoir, both the shale rock's properties and the multistage hydro-fracking technique of the horizontal well should be considered, which is a difficult problem of mechanics. In this paper, the mechanical characteristics of the shale rock and the multistage fracking technology of the horizontal well in the shale gas reservoir are discussed, as well as the applications of the extended finite element method, the boundary element method and the discrete element method in hydraulic fracturing and their advantages and limitations. It is indicated that the three dimensional displacement discontinuity method of the boundary element method is an effective approach to model the propagation of multistage fractures.