The energies of surface states as functions of a parameter γ, which measures the electron affinity of a surface atom relative to an atom in the interior of the crystal, are calculated for a one-dimensional δ-well chain. The treatment is extended to a three-dimensional simple cubic lattice by using a modified free electron network model. Depending on γ, surface bands can exist in the energy gaps between the volume bands, or a surface band may overlap and lose any number of states to the volume bands below it. Only the lowest volume band, derived from the single bound state of the isolated δ-well, can give rise to a surface band of lower energy.