Analytical solutions are presented for the deformation and stress state of a horizontally stratified earth subject to normal loads of size and wavelength that are characteristic of seamounts. The models investigated include layered elastic plates, homogeneous viscoelastic plates, and elastic over viscoelastic models. In all cases the composite models overlie an inviscid half space. The principal advantage of the laminated elastic models over homogeneous elastic plates is that they can result in a substantial reduction in the maximum stress differences in those parts of the plate least capable of supporting large stress differences. A number of geophysical observations point to stress relaxation when the lithosphere is loaded on geological time scales, and this has been modeled with viscolastic and elastic-viscoelastic models. The viscoelastic models explain many of these observations, but the stresses remain unrepresentative of those in the real lithosphere. The elastic-viscoelastic models, in which the parameters defining each layer are considered as effective moduli or viscosities, represent better the rheological zonation of the earth with the crust being modeled by one or several elastic layers, the subcrustal lithosphere by a viscoelastic layer, and the mantle by an inviscid fluid. Observation of gravity or geoid height over the seamounts cannot readily discern between the viscoelastic and elastic-viscoelastic models unless detailed observations over the moat and arch are available. A summary of some estimates of effective flexural rigidity indicates that the stress relaxation is an important factor in determining the response of the lithosphere to loading.