Extending the Gaussian model of solvation (Chandler, D. Phys. ReV. E 1993, 48, 2898) to dynamics, we focus specifically on the problem of dielectric relaxation. In the Gaussian model, the solvent is described in terms of a linear responding field that is expelled from the volume occupied by the solute. The excluded volume affects the normal modes of the system, thereby playing a significant role in solvation dynamics. Even in the context of dielectric continuum theory, the excluded volume affects the polarization response outside that volume. We show that this effect can be analyzed generally and analytically.