A model for treating solute polarizability in solvation processes is presented. The model, which requires little computation compared to atomic detail simulations, is based on a classical electrostatic treatment, whereby the solute polarizability is represented by local dielectric constants (LDC) rather than the usual point inducible dipoles. Point inducible dipoles and local dielectric constants are shown to be formally equivalent ways of representing solute polarizability for a simple spherical, point dipolar solute. For more realistic solute representations, however, there are some advantages to the local dielectric model. The solvation energy, change in solute dipole moment upon polarization, and the polarization energy in the LDC model are obtained self-consistently from one set of calculations involving solutions to the Poisson equation. Calculated solvation energies are compared to experimental data for water and 12 small polar solutes.