In the present study, the rotation of material axes on the free bending vibrations response of a certain type of composite "Bonded and Stiffened System" is theoretically analyzed and numerically solved with some numerical results. The composite "Bonded and Stiffened System" is composed of a "Mindlin Base Plate or Panel" reinforced by three "Bonded Stiffening Plate Strips". In the analysis, the 90 rotation effects of the material axes on the natural frequencies and the mode shapes of the entire "System" are investigated. The aforementioned "Bonded and Stiffened System" is considered in terms of the "System.1" and the "System.2". In the "System.1", the material axes of the "Base Plate" are rotated 90 (about z-axis), while there is no change in the material axes of the "Bonded Plate Strips". In the "System.2", there is no change in the material directions of the "Base Plate", while the material axes of the "Bonded Plate Strips" are rotated 90 degrees. The "Base Plate or Panel" and the three "Bonded Plate Strips" are assumed to be dissimilar "Orthotropic Mindlin Plates". The in-between, relatively very thin, linearly elastic adhesive layers are considered with different material characteristics. All "Mindlin Plate Elements" of both "Systems.1 and 2" are included in the analysis with the transverse (or bending) moments of inertia and rotary moments of inertia. The dynamic equations of the "Mindlin Plate Elements" and the in-between adhesive layer expressions (with the transverse normal and shear stresses) are combined togather. After some algebraic manipulations and combinations, they are eventually reduced to a set of the "Governing System of the First Order O.D.E's" in compact matrix forms with the "state vectors" for each case of the "System.1" and "System.2". The aforementioned "Governing Equations" facilitate direct application of the present method of solution that is the "Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)". The "Governing Equations" are numerically Integrated by means of the "(MTMM) (with Interpolation Polynomials)". The natural frequencies and the mode shapes of the "Systems.1 and 2" are computed and graphically presented for some "Support Conditions" of the "Systems" under consideration. The comparison of the numerical results led to some important conclusions.