We develop analytical solutions for analyzing viscous relaxation of a compressible mantle to surface loading. Two different models are considered: one in which the density step of the core-mantle boundary (CMB) is held fixed and the other in which the mass of the Earth remains invariant with respect to variations of equation of state parameters. For thermodynamic parameters characteristic of the mantle, relaxation times of the fundamental and first overtone modes change by no more than about 30% for degree less than 4. For a given initial depression, the ratio between the velocity in the lower mantle and that at the surface is bigger for imcompressible models than for compressible models. Eigenfunctions between the two models also differ in appearance throughout the mantle, with the incompressible ones being larger for the second model. These results would suggest that the resolution of mantle viscosity may be impaired by the smaller excitation in the lower mantle due to effects of mantle compressibility. ¿ American Geophysical Union 1987