Micromechanisms of rock failure (axial splitting and shear failure) are examined in light of simple mathematical models motivated by microscopic observations. The elasticity boundary value problem associated with cracks growing from the tips of a model flaw is solved. It is shown that under axial compression, tension cracks nucleate at the tips of the preexisting model flaw, grow with increasing compression, and become parallel to the direction of the maximum far-field compression. When a lateral compression also exists, the crack growth is stable and stops at some finite crack length. With a small lateral tension, on the other hand, the crack growth becomes unstable after a certain crack length is attained. This is considered to be the fundamental mechanism of axial splitting observed in uniaxially compressed rock specimens. To model the mechanism to shear failure, a row of suitably oriented model flaws is considered and the elasticity boundary value problem associated with the out-of-plane crack growth from the tips of the flaws is solved. It is shown that for a certain orientation of the flaws the growth of the out-of-plane cracks may become unstable, leading to possible macroscopic faulting. On the basis of this model the variations of the ''ultimate strength'' and the orientation of the overall fault plane with confining pressure are estimated, and the results are compared with published experimental data. In addition, the results of a set of model experiments on plates of Columbia resin CR39 containing preexisting flaws are reported. These experiments are specifically designed in order to show the effect of confining pressure on the crack growth regime. The experiments seem to support qualitatively the analytical results.