Abstract: According to the determination of the rock pressures and collapse mechanisms of tunnels, the finite element upper-bound method with rigid translatory moving elements (UBFEM-RTME) is used to obtain the upper bound solution charts of the supporting force coefficients N_γ and N_c as well as collapse mechanisms with active discontinuities and evolution laws. Compared with a wide variety of the upper bound rigid block method (UBRB) assuming collapse mechanisms and the simulation model tests, it is verified that the upper limit solution of the support force obtained by the UBFEM-RTME method is the optimal solution in the theoretical framework of the upper bound limit analysis. At the same time, the upper bound solutions of N_γ and N_c are consistent with the trend of the rock pressure solutions of the Terzaghi theory. In addition to the upper solutions of N_γ and N_c, the UBFEM-RTME method has many morphological features in the collapse mechanisms with active discontinuities, and basically covers different types of failure mechanisms in the existing literatures. It is shown that the UBFEM-RTME method can get rid of the limitation of the assumed collapse mechanisms and has great applicability and superiority for solving the rock pressures of the tunnels.