Two mainly used methods of investigation have been established in discrete-continual approach to analysis of deformations of ribbed plates. One of them is based on the conception of singularly heterogeneous body, and that allows us to reduce the problems under consideration to solution of differential equations whose coefficients depend on the function and its derivatives. The other approach is based on the method of `gluing’. Among different versions of this method, the better seems to be the one, which is based on decomposition of an elastic system into the smallest elements. This method allows us to reduce the problems differential-difference equations. We follow the second direction, and our purpose is to study free vibrations of rectangular in plane cylindrical panels with unidirectional stringers and structurally orthotropic casing. Based on the sufficiently general assumptions on geometrical and elastic properties of the panels, a corresponding differential-difference eigenvalue problem is stated. In the case when the panel is simply supported at its curvilinear edges (which are perpendicular to the stringers) this problem can be reduced exactly to a discrete (difference) eigenvalue problem, the numerical solution of which is illustrated by examples.