The dielectric response is considered within models of a one-band metal, a two-band insulator and a two-band metal using the semi-classical approximation. Corresponding dielectric functions are found. The dielectric function of two-band metal is found to be the interpolation between the Sellmeyer and Lorenz-Lorentz expressions, respectively. The frequencies of the collective modes are identified as the zeroes of the dielectric functions. The correspondence between the semi-classical approach used in this paper and the many-body calculation within the random-phase approximation is established.