Triaxial loading of certain rocks sometimes results in faulting without fracture in the ordinary sense, or sudden displacements. A brief discussion of the theory of brittle fracture of Griffith is given to indicate why it cannot apply to this kind of ductile faulting. Such ductile faulting can be explained by the theory of plasticity for plane strain. This theory is presented for more general yield conditions than that of von Mises, and it is assumed that the stress-strain rate relations can be derived from the yield condition by a process of differentiation. This formalism is by no means original, but it is little known among geologists. Across certain planes in the plastic mass, discontinuities in the velocity are possible, whereas the stresses remain continuous across these planes. These "characteristic planes" of the velocity equations are identified with the planes of ductile faulting. The results obtained in the theory of plane strain for the von Mises, Coulomb, and Torre yield conditions do not hold for the more general three-dimensional theory, unless very stringent conditions on the strain rates are satisfied. Smooth characteristic surfaces in the plastic domain are possible only if these conditions are satisfied. Possibly, however, there are yield conditions which lead to smooth characteristic surfaces under weaker restrictions on the strain rates.