Natural barrier systems surrounding the geological repository for the high-level radioactive waste should guarantee the hydraulic performance for preventing or delaying the leakage of radionuclide. In the case of the behavior of a crystalline rock, the hydraulic performance tends to be decided by the existence of discontinuities, so the coupled hydro-mechanical (HM) processes on the discontinuities should be characterized. The discontinuum modelling can describe the complicated behavior of discontinuities including creation, propagation, deformation and slip, so it is appropriate to model the behavior of a crystalline rock. This paper investigated the coupled HM processes in discontinuum modelling such as UDEC, 3DEC, PFC, DDA, FRACOD and TOUGH-UDEC. Block-based discontinuum methods tend to describe the HM processes based on the fluid flow through the discontinuities, and some methods are combined with another numerical tool specialized in hydraulic analysis. Particle-based discontinuum modelling describes the overall HM processes based on the fluid flow among the particles. The discontinuum methods that are currently available have limitations: exclusive simulations for two-dimension, low hydraulic simulation efficiency, fracture-dominated fluid flow and simplified hydraulic analysis, so it could be improper to the modelling the geological repository. Based on the concepts of various discontinuum modelling compiled in this paper, the advanced numerical tools for describing the accurate coupled HM processes of the deep geological repository should be developed.