A new class of multilayered, viscoelastic Earth models based on PREM, with an incompressible, linear, viscoelastic Maxwell rheology, is applied to the modeling of co-seismic and post-seismic deformation following large earthquakes. The novelty of our approach stands on the usage, for the first time in post-seismic studies, of a fully analytical scheme based on normal mode theory that allows to deal with some of the complexities of the real Earth, such as lithospheric and mantle layering, sphericity and self-gravitation. For a dip-slip source, used as a test case, elastic layering of the lithosphere is necessary for the modeling of realistic patterns of post-seismic deformation, although only a few layers, namely three, are sufficient to reproduce correct deformation patterns, in consequence of the fact that below the crust, the lithosphere inferred from PREM is rather homogeneous. The viscosity structure of the mantle has a major influence on post-seismic deformation in the far field, at distances from the epicenter of the order of 100 km. At least for lithospheric sources, precise modeling of post-seismic deformation does not require for the mantle the same fineness of layering that is necessary for the lithosphere. Our findings are key for future analyses of the co-seismic and post-seismic effects of large earthquakes, in view of a correct interpretation of VLBI, GPS and Satellite Differential Radar Altimetry data.