(Accepted for publication June 8, 1978) ABSTRACT: Recent geodetic data indicate that the earth exhibits systematic long-term nonseismic deformation. Numerous examples of this behavior can be found in both local precursory and postseismic displacements, and in glacial rebound. In many cases, the best way to explain the observed motion is with the use of earth models consisting of a brittle region overlying a more ductile, easily deformable zone. A widely used method for construction of theoretical models to explain the observed deformation is the Green's function technique. With this method, either the displacements or stresses over surfaces of displacement can be readily specified. Modern data-inversion theory can be employed and the values of physically meaningful parameters in the earth model can be determined. An example of such an anelastic earth model is presented. The model consists of an elastic layer over a viscoelastic half-space. It is shown how the quasistatic viscoelastic response to a fracture occurring in the elastic layer can be computed by two mutually comparible techniques, both of which are accurate and convenient to use. As an example, a model of the 1906 San Francisco earthquake is presented and it is shown that the model fits the data well.