The problem of the free flextural vibrations of a rectangular, orthotropic composite plate or panel system composed of an orthotropic base plate and a dissimilar central stiffening plate strip joined by a thin adhesive layer, is studied. In the formulation, both plates are assumed to be dissimilar orthotropic plates in the manner of the Mindlin Plate Theory. The composite plate or panel system has two opposite edges as simply supported while the other two opposite edges can have arbitrary support conditions. First, classical “Levy Type Solutions” are used for the displacements angle of rotations and the stress resultants. Then, the resulting governing equations of the problem are integrated by a “Modified Version of the Transfer Matrix Method”. The mode shapes and corresponding natural frequencies of the composite plate system are studied for “hard” and “soft” adhesives. It was shown that the normal mode shapes and natural frequencies are very much influenced by the adhesive layer material constants. Also, some parametric studies are presented.