A numerical code called Rock Failure Process Analysis (RFPA2D) was employed to investigate the closure, damage and failure behavior of the horizontal tunnels. In his code the time-dependent deformation was described in terms of evolution of mesoscopic structure, leading to progressive degradation of elastic modulus and failure strength of material. In terms of material degradation, a series of numerical simulations were performed to study the convergence and subsequent failure in circular tunnels. The numerical esults provide a complete illumination for the closure, damage and failure behavior with different loading conditions. It is shown that the depth and the ratio of far field stresses play an important role in the creep behavior of tunnels. Creep failure is expected to occur in the direction of the smallest far field stress component, which means that rheological failure of tunnels is influenced not only by the rock characteristic around the tunnels but also by the orientation and distribution of far field stress on a global scale.