An original method to compute the steady state forced response of linear systems with periodically varying parameters under external excitations is proposed. The procedure is based on a modal approach with developments in the frequency domain. By using an iterative scheme to construct the approximate response, the spectra and the root mean square values of the forced response at every degree of freedom can be directly obtained. The technique has been successfully tested on illustrative examples and compared to the standard Newark method. Its efficiency is a consequence of the very short computing times needed. A practical application concerning a geared transmission system which is excited by periodic meshing stiffness is presented to demonstrate that this method is very effective in analyzing systems having many degrees of freedom.