Over the past twenty years, there has been a growing interest in the development of numerical models that can realistically capture the progressive failure of rock masses. In particular, the investigation of damage development around underground excavations represents a key issue in several rock engineering applications, including tunnelling, mining, drilling, hydroelectric power generation, and the deep geological disposal of nuclear waste. The goal of this paper is to show the effectiveness of a hybrid finite-discrete element method (FDEM) code to simulate the fracturing mechanisms associated with the excavation of underground openings in brittle rock formations. A brief review of the current state-of-the-art modelling approaches is initially provided, including the description of selecting continuum- and discontinuum-based techniques. Then, the influence of a number of factors, including mechanical and in situ stress anisotropy, as well as excavation geometry, on the simulated damage is analysed for three different geomechanical scenarios. Firstly, the fracture nucleation and growth process under isotropic rock mass conditions is simulated for a circular shaft. Secondly, the influence of mechanical anisotropy on the development of an excavation damaged zone (EDZ) around a tunnel excavated in a layered rock formation is considered. Finally, the interaction mechanisms between two large caverns of an underground hydroelectric power station are investigated, with particular emphasis on the rock mass response sensitivity to the pillar width and excavation sequence. Overall, the numerical results indicate that FDEM simulations can provide unique geomechanical insights in cases where an explicit consideration of fracture and fragmentation processes is of paramount importance.