The work contained in this thesis considers deformations of the Earth, which are produced by the loads of the last ice-age glacial sheets. The forces the Earth sets against the surface loads are the buoyancy force of the Earth's mantle and the opposing force by the elastic flexure of the lithosphere. Because the time scale of the ice-age of some 100,000 years is short with respect to geological time scales, the viscoelastic behaviour of the Earth has to be considered. Viscoelasticity results in a retarded response of the Earth, which is observed as postglacial uplift in previously glaciated regions, 8,000 years after deglaciation. To model the buoyancy of the Earth's mantle, often a viscous incompressible fluid of homogeneous density is assumed. More recent studies consider also compressibility of the mantle material, but keep the homogeneous density. This results in an inconsistent reference state, because the self compression due to hydrostatic pressure is neglected. These models are discussed here, and the problems are shown, which arise from the description of the field equations for a viscoelastic compressible gravitating continuum in a half-space geometry. The opposing force by the elastic flexure of the lithosphere is determined by the flexural rigidity of the lithospheric plate. If we consider viscoelastic layers in the lithosphere, the flexural rigidity is reduced. Therefore, the overall thickness of a viscoelastic layered lithosphere is much larger than its effective elastic thickness deduced from assuming one elastic plate. Consequently the effective elastic thickness looses its merit for assessing the lithosphere thickness. We show, how strong effective elastic thickness and lithosphere thickness may differ, in which way the viscoelastic structure of the Earth influences this difference for glacial loads and which consequences arise for the lithospheric stress state.