Laboratory experiments were conducted in order to find effects of the intermediate principal stress of σ2 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 σ3 and σ2 were maintained constant, and the maximum stress σ1, 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 σ2 = σ3. Compressive rock failure took the form of a main shear fracture, or fault, steeply dipping in σ3 direction with its strike aligned with σ2 direction. Rock strength rose significantly with the magnitude of σ2, suggesting that the commonly used Mohr-type failure criteria, which ignore the σ2 effect, predict only the lower limit of rock strength for a given σ3 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 σ2. Thus, σ2 extends the elastic range for a given σ3 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 σ1-σ2 plane as the magnitude of σ2 is raised.