A discrete element model is proposed to examine rock strength and failure. The model is implemented by UDEC which is developed for this purpose. The material is represented as a collection of irregular-sized deformable particles interacting at their cohesive boundaries. The interface between two adjacent particles is viewed as a flexible contact whose stress-displacement law is assumed to control the material fracture and fragmentation process. To reproduce rock anisotropy, an innovative orthotropic cohesive law is developed for contact which allows the interfacial shear and tensile behaviours to be different from each other. The model is applied to a crystallized igneous rock and the individual and interactional effects of the microstructural parameters on the material compressive and tensile failure response are examined. A new methodical calibration process is also established. It is shown that the model successfully reproduces the rock mechanical behaviour quantitatively and qualitatively. Ultimately, the model is used to understand how and under what circumstances micro-tensile and micro-shear cracking mechanisms control the material failure at different loading paths.