This paper investigates the relationships between hillslope stability and fabric anisotropy of brittle rock materials and the implications for landscape shaping. We use discrete element models to study the stability and failure modes of slopes made of transverse isotropic rock materials, focusing more particularly on the influence of the material orientation relative to the topographic slope. After validating the numerical approach with a limit equilibrium analytical solution in the case of an isotropic material, we modify our numerical slope models to simulate the rheological features of anisotropic gneissic rocks. Systematic exploration of the transverse isotropy plane's orientation in two dimensions (dip angle) reveals that slope collapse requires strength values that are highly dependent on the orientation of the material relative to the slope. For a 1000 m high escarpment, the stability of a slope with a fixed gradient requires strength that is one order of magnitude greater in a configuration where the isotropy plane is slightly less inclined than the topographic slope (i.e., cataclinal overdip configuration) than in a configuration where the isotropy plane is perpendicular to the slope (i.e., anaclinal configuration). Mirroring this highly variable stability according to the relative orientation of the material, four modes of deformation or gravitational instability are observed: in order of appearance, when the transverse isotropy plane orientation goes from 0 to 180° with respect to the horizontal (going from cataclinal to anaclinal configurations), the slope collapses respectively by sliding, buckling, toppling and crumbling. The crumbling mode corresponds to a very stable configuration for which the preferred ground movements will be rock falls from the cliff compared to the structurally controlled, deep-seated deformation modes leading to sliding and toppling. Despite the simplifications inherent to the numerical approach, our study highlights the essential characteristics of landslides occurring along slopes cut in transverse isotropic materials and reproduces the various instability modes observed in natural slopes. It also enables assessing their respective kinetics as well as the volumes of material they mobilize. Finally, by comparing our findings on the azimuthal variations in hillslope gradients observed along the central Himalaya (Nepal), in an area characterized by the relatively uniform orientation of the anisotropy in gneissic and mica-schist formations, we show that, even though multiple environmental factors come into play, landscape shaping is indeed strongly controlled by material anisotropy.