In this paper, a discrete-finite element method (DFEM) is formulated and then applied to solve problems arising in the process of underground tunnel excavation in rock mass with faults, which involved elasto-visco-plasticity and brittleness of rock mass and large deformation and discontinuous displacement (sliding, toppling, and fractures, etc.). The idea employed in the DFEM is as follows. The domain of interest (Omega) is divided 'adaptively' into two parts according to certain fracture rules, the continuum domain (Omega) con, and the domain of discrete block domain (Omega) dis in which large displacement and discontinuity (fractures) may occur and propagate according to certain fracture criteria. This method uses both the local static relaxation (SR) method and the dynamic relaxation (DR) method in (Omega) dis, while the traditional FEM, which can be explained as a global static relaxation method, within each discrete block in (Omega) dis and the continuum domain (Omega) con as well. By coupling these two methods within boundary elements in (Omega) dis and on the continuum boundary (partial)(Omega) dis (partial)(Omega) con, we can obtain a global iteration scheme which converges to an equilibrium state. The method has almost the same complexity as that of the hybrid method of DEM and FEM. However, it models the fracture process more naturally. A mathematical explanation of the result is that the method produces a min - max solution to the problem.