The influence of the intermediate principal stress on rock strength has been studied comprehensively by previous researchers. However, the reason why rock strength firstly increases and subsequently decreases with the increase of intermediate principal stress is still unclear. In this paper, the mechanism of the intermediate principal stress effect on rock failure behaviour is revealed through a numerical method using the EPCA3D system (Elasto-Plastic Cellular Automaton). In this study, both homogeneous and heterogeneous rocks are considered. The heterogeneity of a rock specimen is modelled by introducing Weibull's statistical distribution. Two criteria, i.e. the Drucker–Prager and Mohr–Coulomb models, are used to determine whether a meso-scopic element in the rock specimen is in a failure state or not during the polyaxial stress loading process. The EPCA3D simulation reproduces the typical phenomenon of the intermediate principal stress effect that occurs in some rock experiments. By studying the EPCA3D simulated acoustic emission and complete stress–strain curves illustrating failure initiation, propagation and coalescence in the failure process of rocks, the essence of the intermediate principal stress effect is tracked. It is concluded that the heterogeneous stress distribution induced by the natural heterogeneity of rocks and the effect of the loading platen are two of the reasons producing the intermediate stress effect. Studies indicate that a moderate intermediate principal stress delays the onset of local failure, which in turn leads to an increase in the rock strength. However, once the intermediate principal stress reaches a certain value, local failure will be formed through the application of the intermediate principal stress. It is the number of failed elements in the pre-peak region that determines whether the rock strength decreases or not. The extent of rock strength reduction when the intermediate principal stress reaches a certain value is lessened with the increase in the minimum principal stress