Using the time dependent density functional method we investigate the effects of a dielectric core and a dielectric embedding medium on the optical properties of metallic nanoshells. The polarizability is shown to be strongly influenced by the presence of the dielectric which induces additional screening charges that need to be included self-consistently. We show that the energies of the dipolar plasmon resonances depend strongly on the dielectric constant of the core or embedding medium, The results compare very well with classical Mie scattering theory calculations. (C) 2002 Elsevier Science B.V. All rights reserved.