Two distinct modes of compressive brittle-like failure are observed in laboratory samples of rock and ice. Under low to moderate confinement, terminal failure follows microcrack growth and interaction when damage is localized along a fault oriented ∼30° to the greatest compressive stress. Under higher confinement, frictional sliding is suppressed, and sudden, localized, brittle-like failure is not attended by a concentration of microcracks near the main fault. Also, faults that form under higher confinement are narrower and oriented ∼45° to the greatest compressive stress. We propose that these more steeply inclined faults are plastic faults whereby deformation is localized because of an instability that develops when thermal softening exceeds strain hardening. Analysis leads to a quantitative model for the shear stresses required to initiate and maintain the instability and to accommodate slip along the fault. The required stress is in general agreement with observed failure stresses from a variety of crystalline materials. Application of this model suggests that in some cases plasticity, rather than friction, limits the strength of the Earth's upper crust.