Strength and ductility of ordinarily brittle substances are commonly observed to increase with mean pressure. However, since the pioneering work of von Kármán and of Böker fifty years ago, it has been recognized that the effects differ from compression (σ1 > σ2 = σ3) to extension (σ3 < σ2 = σ1) tests, where subscripts denote maximum, intermediate, and minimum principal (compressive) stresses. This difference has been ascribed to the influence of σ2, but, to our knowledge, it has not previously been quantitatively demonstrated. By subjecting jacketed cylinders to combined triaxial compression or extension and torsion, one can obtain relative values of σ2 that lie between the limits σ2 = σ1 and σ2 = σ3; in torsion alone σ2 lies midway between. The data from different types of test are conveniently compared by plotting octahedral stress τoct against mean pressure Pm at fracture or yielding. Tests have been done at temperatures of 25 to 500°C, confining pressure to 10 kb, and different strain rates (10−4 to 10−7 per second) on 1‐ by 2‐cm solid cylinders and 1.2‐ by 2.5‐cm hollow cylinders (0.7‐mm wall) of homogeneous, statistically Isotropic Solenhofen limestone, Blair dolomite, and glass. At strain rates near 10−4 per second at 25°C, the τoct versus Pm curves for limestone are essentially linear and reflect brittle behavior at relatively low pressures. In compression, failure occurs by shear fracturing; in extension and torsion, tensile fracture dominates. The shear strength is dependent upon mean pressure but tensile breaking strength is not. At intermediate pressures the curves become concave toward the Pm axis. This is associated with transitional behavior, faulting in all three types of test. This brittle‐ductile transition occurs at 2.7 and 5.4 kb in compression and extension, respectively; in torsion it is near 4.0 kb. This strongly suggests that ductility is a linear function of the relative magnitude of the intermediate principal stress. At high pressures all curves tend to approach the same asymptote, τoct = constant. The results for dolomite and glass are similar. Increasing the temperature or decreasing the strain rate tends to lower the transition confining pressures for all states of stress.