Strike-slip faulting in the crust and its mechanical interaction with the underlying mantle is presented as the basis for an earthquake and aftershock mechanism. The usual problem of a fault in a homogeneous half space is a special case of the present model, where both layering and time-dependence play an important role. The system is characterized by a three-dimensional problem in static linear elasticity and viscoelasticity, where the fault is represented by a vertical Volterra disclocation in the layer with slip parallel to the surface. Both materials are assumed to be incompressible. The problem is solved by means of a modified form of the Galerkin vector and use of double Fourier transforms, and solutions are obtained in quadrature for the surface displacements and some of the stresses at the interface. Time-dependent properties are introduced formally into the quadrature by use of the correspondence principle of linear viscoelasticity.