We present a theoretical model to study the dynamics of metallic clusters embedded in a rare gas matrix. We describe the active electrons of the embedded cluster using time dependent density functional theory, while the surrounding matrix is described in terms of classical molecular dynamics of polarizable atoms. The coupling between the cluster and the rare gas atoms is deduced from the work of Gross and Spiegelmann [J. Chem. Phys. 108, 4148 (1998)] and reformulated explicitly in a simple and efficient density functional form. The electron rare gas interaction takes the form of an averaged dipole fluctuation term, which retains the van der Waals long range interaction, and a short range repulsive pseudopotential, which accounts for the Pauli repulsion of the electron by the rare gas atom. We applied our model to Na clusters embedded in Ar matrix. For the latter we developed an efficient local pseudopotential, which allows studying systems containing more than 10(3) Ar atoms. We show that large systems are indeed necessary to account properly for long range polarization of the matrix, that competes with the matrix confinement effect. We focus our study on Na-2, Na-4, and Na-8. For each system, we have determined the geometry of the most favorable trapping site by means of damped molecular dynamics. We present the effect of matrix embedding on the optical absorption spectrum. For Na-2, the trapping site can be unambiguously identified by comparison of the absorption spectrum with experiment. For Na-4 the spectrum of the embedded cluster is significantly different from the free cluster spectrum, while for Na-8 differences are less pronounced. (C) 2004 American Institute of Physics.