A continuum model of nonpolar solvation is presented. Coupling of the solute to the solvent is assumed to occur through a change in the solute's size or shape upon electronic excitation. Both spherical and nonspherical changes in the solute are treated. The time-dependent shear and longitudinal moduli of the solvent determine the solvation response function. Unlike prior continuum models of solvation, both a rapid, viscosity-independent inertial component and a slower, viscosity-dependent diffusive component emerge from the model, even when only one time scale is assumed in the moduli. The origin of multiple time scales in this model, which has a single solvent coordinate with complex dynamics, is contrasted with treatments such as the multimode Brownian oscillator models, which postulate multiple solvent coordinates, each with simple dynamics.