A procedure is given for including the rearrangement energy term in the Brueckner-Gammel method for evaluating the structure of finite nuclei. A variational technique is used to derive the single-particle energy from the total binding energy of the nucleus. It is seen that although a rearrangement energy term does not appear explicitly in the total nuclear binding energy, it is derivable from the binding energy and influences the eigenfunctions of the total nuclear system, and thus its energy eigenvalues. The rearrangement energy has a noticeable effect on the single-particle wave equation and must be included in finite nucleus calculations. To a good approximation, it is shown that it is possible to evaluate the rearrangement potential and to express it as a simple function of the mean nuclear density, i.e., VR=(240 Mev)ρ2×(10- 13 cm)6.