Frictional slippage on material interfaces is pervasive in mechanical problems of all types, but it can be particularly important in geomechanics. Extent models of cracked or jointed rock usually take frictional resistance along rock interfaces to be described by uniform Coulomb friction. A simple theory is presented which incorporates nonuniform friction. The description is by means of continuous distributions of infinitesimal dislocations. The resulting stress-plastic strain behavior is nonlinear and stress history dependent and is a result of the generation, interaction, and annihilation of slip zones of unlike sign. The theory provides an explanation for the discrete memory effect observed during cyclic stressing of rock and also indicates potential difficulties in the design and interpretation of experiments on jointed rock.