The strengths of rocks clearly place an upper limit on the stress that can be sustained by the upper half of the lithosphere. Laboratory data on rock rheology are generally lacking at intermediate temperatures and pressures on the important rock types expected in the lithosphere, so a definitive accounting of the strength distribution with depth in the upper lithosphere is presently unattainable. Analogies are drawn between the fragmentary strength data on silicates at intermediate temperature and the more extensive experimental data on marble and limestone, and several tentative conclusions are drawn: First, brittle processes, such as faulting and cataclasis, are expected to control rock strength at low pressures and temperatures. The strengths associated with these brittle mechanisms increase rapidly with increasing effective pressure and are relatively insensitive to temperature and strain rate. Second, the transitions between brittle and ductile processes occur at critical values of the least principal stress σ₃. I suggest that the concept of the deformation mechanism map of Ashby (1972) be extended to brittle-ductile transitions by normalizing the applied differential stress σ by σ₃, i.e., the transitions occur at critical values of σ/σ₃. Third, the high temperature flow law of olivine, widely applied to problems involving flow in the asthenosphere, is inappropriate to the conditions of temperature found in the lithosphere, because different dislocation flow mechanisms dominate at low to intermediate temperatures. The fragmentary rheological data suggest the following rheological structure of the lithosphere where it is inelastically deforming: A rapid pressure-driven increase in rock strength with depth culminates with a shear strength maximum of up to 8 kbar at depths that depend on the state of stress and on the temperature distribution. A review of the mechanisms of weakening associated with water suggests that water weakening effects are probably not important in the oceanic lithosphere but are likely to be controlling in the continental crust.