This paper presents the development of a three‐dimensional discrete element model using flat‐joint and smooth‐joint contact models to investigate the effect of anisotropy on the tensile behaviour of slate, a transversely isotropic rock, under Brazilian testing from both macro and microscales. The effect of anisotropy is further realised by exploring the influence of foliation orientations (β and ψ ) on the tensile strength, fracture pattern, microcracking and stress distribution of the transversely isotropic rock. The variation of tensile strength with foliation orientation is presented. The cross‐weak‐plane fracture growth observed in laboratory is reproduced, and the criterion for which to form is also given from the aspect of foliation orientation. Furthermore, the proportional variations of microcracks well account for the effects of foliation orientation on the tensile strength and failure pattern. Finally, it is found that the existence of weak planes increases both the heterogeneity and the anisotropy of stress distributions within the transversely isotropic rock, with the degree of influence varying with the foliation orientation.