In the present paper, the mechanical behaviour of fibre-reinforced brittle-matrix composites, with emphasis to cementitious composites, is examined by adopting both a discontinuous- like FE approach and a lattice model. The main phenomena involved, such as crack formation and propagation, crack fibre bridging, fibre debonding, fibre breaking, are taken into account. The basic assumptions and theoretical background of such approaches are outlined, and some experimental data related to plain and fibre-reinforced concrete specimens under Mode I and Mode I + II loading are analysed. The comparison of the numerical simulation results shows that the lattice model allows us a very detailed description of the fracture pattern, whereas the discontinuous FE approach mainly gives us only global information in terms of both crack path and stress–strain response curve. Nevertheless, the FE approach is computationally convenient and a useful tool for studying problems which do not require a detailed description of the fracture process.