This chapter examines failure criteria for brittle anisotropic rocks, emphasizing their implications under varying stress conditions. It critiques traditional theories like maximum stress and maximum strain for their limited applicability to anisotropic materials. The linear Mohr’s envelope is explored as an empirical tool suited for compressive stress scenarios in anisotropic rocks. The Griffith theory emerges as pivotal for understanding tensile failure, suggesting potential extensions to incorporate anisotropic considerations. The chapter distinguishes between shear failure in isotropic materials and the complex failure modes influenced by cleavage planes in anisotropic rocks, where fracture angles vary significantly based on plane orientation relative to stress direction. It introduces Jaeger’s approach based on the Coulomb-Navier theory to unify these modes of failure, detailing equations that predict failure across and along cleavage planes. Practical examples illustrate how these concepts apply in compression and tensile tests, highlighting transitional angles and critical orientations of cleavage planes affecting material strength. Figures throughout provide visual aids to aid comprehension of these concepts.