Laboratory experiments were conducted in order to find effects of the intermediate principal stress of ${sigma}_{2}$ on rock fractures and faults. Polyaxial tests were carried out under the most generalized compressive stress conditions, in which different magnitudes of the least and intermediate principal stresses ${sigma}_{3}$ and ${sigma}_{2}$ were maintained constant, and the maximum stress ${sigma}_{1}$, was increased to failure. Two crystalline rocks (Westerly granite and KTB amphibolite) exhibited similar mechanical behavior, much of which is neglected in conventional triaxial compression tests in which ${sigma}_{2}$ = ${sigma}_{3}$. Compressive rock failure took the form of a main shear fracture, or fault, steeply dipping in ${sigma}_{3}$ direction with its strike aligned with ${sigma}_{2}$ direction. Rock strength rose significantly with the magnitude of ${sigma}_{2}$, suggesting that the commonly used Mohr-type failure criteria, which ignore the ${sigma}_{2}$ effect, predict only the lower limit of rock strength for a given ${sigma}_{3}$ level. The true triaxial failure criterion for each of the crystalline rocks can be expressed as the octahedral shear stress at failure as a function of the mean normal stress acting on the fault plane. It is found that the onset of dilatancy increases considerably for higher ${sigma}_{2}$. Thus, ${sigma}_{2}$ extends the elastic range for a given ${sigma}_{3}$ and, hence, retards the onset of the failure process. SEM inspection of the micromechanics leading to specimen failure showed a multitude of stress-induced microcracks localized on both sides of the through-going fault. Microcracks gradually align themselves with the ${sigma}_{1}$-${sigma}_{2}$ plane as the magnitude of ${sigma}_{2}$ is raised.