A method is formulated for the exact calculation of Green functions for finite quasi-static sources in an elastic layer over a linear viscoelastic half space. The displacements due to the same sources in an elastic layer over an elastic half space are first computed, and then the well-known correspondence principle of linear viscoelasticity is applied. The most difficult part of the problem, the inversion into the time domain, is accomplished by means of a novel technique. As a first example of the mothod, the growth of the error in an approximate Green function for a strike slip source is evaluated. Second, the viscoelastic uplifts due to an expanding sphere are calculated for two half-space rheologies. Third, the time dependent uplifts due to point dip slip-sources are computed. Finally, the dip slip Green functions are integrated over a finite rectangular fault surface, and the coseismic and postseismic uplifts are compared.