Realistic computer models of fracture-block systems have signiยฎcant impacts on the performance of DEM models of fractured rocks, especially for near-ยฎeld coupled hydro-mechanical problems. In this paper, the basic components of an algorithm for establishing geometry of block systems of fractured rocks for discrete element methods are presented. The algorithm is based on the basic principles of combinatorial topology. It uses a boundary chain operator for block tracing, using fracture intersection data, and the EulerยฑPoincaร re formula of polyhedra for ensuring the correctness of the tracing operations. Eort was made to simplify the presentation of the theory and techniques without introducing too many concepts and principles of combinatorial topology. The main advantage of this new algorithm is that its capability to deal with any complex geometry of natural rock fracture systems of ยฎnite sizes and arbitrary shapes, therefore it is able to represent more realistically the fracture system connectivity and block system formation for coupled hydro-mechanical analyses using DEM models. The disadvantage of using inยฎnitely large fractures for block system generation, which tends to overestimate the fracture connectivity, can therefore be avoided.