|Abstract||This paper puts forward a general compressive strength criterion for anisotropic rock materials under multiaxial state of stress. The proposed criterion, is a generalization of the Von Mises yield criterion for ductile metals, which criterion has previously been used for brittle fracture as well, both being looked upon as limits of linear elastic behaviour. The proposed criterion takes into consideration the effects, on rock material failure under multiaxial stress state, of confining pressure, presence of various stress components, and material anisotropy. Relevant failure envelopes, for several types of rock materials, are compared with corresponding experimental results; close agreement being obtained in all cases. This result confirms the versatility and applicability of the proposed strength criterion in representing the compressive strength behaviour of anisotropic rock materials under complex multiaxial state of stress.