We introduce a continuum model for impurity modes of Frenkel excitons in fully occupied face-centered and body-centered cubic lattices with dipole-dipole interactions and parallel moments. In the absence of impurities, the model reproduces the small-k behavior found in numerical calculations of dipolar lattice sums. The exciton densities of states near the upper and lower band edges are calculated and compared with the corresponding results for a random array of dipoles. The Green function obtained with the continuum model, together with a spherical approximation to the Brillouin zone, is used to determine the conditions for the formation of a localized exciton mode associated with a shift in the transition energy of a single chromophore. The dependence of the local mode energy on the magnitude of the shift is ascertained. The formation of impurity bands at high concentrations of perturbed sites is investigated using the coherent potential approximation. The contribution of the impurity bands to the optical absorption is calculated in the coherent potential approximation. The locations of the optical absorption peaks of the dipolar system are shown to depend on the direction of propagation of the light relative to the dipolar axis, a property that is maintained in the presence of short-range interactions. (C) 2013 AIP Publishing LLC.