[en] The equation-of-motion technique is used within the random-phase-approximation to calculate the plasma frequency of the electron gas at zero temperature in the finite layered model of Visscher and Falicov with free surfaces. The plasma frequencies are given by the eigenvalues of a Toeplitz matrix. This matrix describes the Coulomb coupling between the plasmons which propagate in different layers. It is shown that this matrix splits into two parts: one which corresponds to the cyclic boundary condition imposed on the system of double thickness and the other due to the presence of the surfaces. The first contribution can be exactly diagonalized and the other one can be treated as a small perturbation for a sufficiently large number of layers. The first-order perturbation theory is applied to obtain finite-size corrections to the plasma frequency. (author)