The problem of the free bending vibrations of a composite base plate reinforced by a bonded, non-central stiffening plate strip is considered. The lower composite base plate and the upper non-central stiffening strip are assumed to be dissimilar orthotropic Mindlin plates joined by a very thin and flexible adhesive layer. The entire composite plate or panel system has two opposite edges as simply supported while the other two opposite edges may have arbitrary boundary conditions. The governing partial differential equations are first reduced to a special set of ordinary differential equations in the first order form and, then, they are integrated by the “Modified Version of the Transfer Matrix Method”. The mode shapes and the corresponding natural frequencies of the stiffened composite plate or panel system are obtained for “hard” and “soft” adhesive layer cases. The natural frequencies of the system for several boundary conditions and parameters are studied. It was found that the hardness and the softness of the adhesive layer significantly influence the mode shapes and the corresponding natural frequencies.