In this study, the &ldquo / Free Flexural (or Bending) Vibrations of Stiffened Plates or Panels&rdquo / are investigated in detail. Two different Groups of &ldquo / Stiffened Plates&rdquo / will be considered. In the first group, the &ldquo / Type 4&rdquo / and the &ldquo / Type 6&rdquo / of &ldquo / Group I&rdquo / of the &ldquo / Integrally-Stiffened and/or Stepped-Thickness Plate or Panel Systems&rdquo / are theoretically analyzed and numerically solved by making use of the &ldquo / Mindlin Plate Theory&rdquo / . Here, the natural frequencies and the corresponding mode shapes, up to the sixth mode, are obtained for each &ldquo / Dynamic System&rdquo / . Some important parametric studies are also presented for each case. In the second group, the &ldquo / Class 2&rdquo / and the &ldquo / Class 3&rdquo / of the &ldquo / Bonded and Stiffened Plate or Panel Systems&rdquo / are also analyzed and solved in terms of the natural frequencies with their corresponding mode shapes. In this case, the &ldquo / Plate Assembly&rdquo / is constructed by bonding &ldquo / Stiffening Plate Strips&rdquo / to a &ldquo / Base Plate or Panel&rdquo / by dissimilar relatively thin adhesive layers. This is done with the purpose of reinforcing the &ldquo / Base Plate or Panel&rdquo / by these &ldquo / Stiffening Strips&rdquo / in the appropriate locations, so that the &ldquo / Base Plate or Panel&rdquo / will exhibit satisfactory dynamic response. The forementioned &ldquo / Bonded and Stiffened Systems&rdquo / may also be used to repair a damaged (or rather cracked) &ldquo / Base Plate or Panel&rdquo / . Here in the analysis, the &ldquo / Base Plate or Panel&rdquo / , the &ldquo / Stiffening Plate Strips&rdquo / as well as the in- between &ldquo / adhesive layers&rdquo / are assumed to be linearly elastic continua. They are assumed to be dissimilar &ldquo / Orthotropic Mindlin Plates&rdquo / . Therefore, the effects of shear deformations and rotary moments of inertia are considered in the theoretical formulation. In each case of the &ldquo / Group I&rdquo / and &ldquo / Group II&rdquo / problems, the &ldquo / Governing System of Dynamic Equations&rdquo / for every problem is reduced to the &ldquo / First Order Ordinary Differential Equations&rdquo / . In other words the &ldquo / Free Vibrations Problem&rdquo / , in both cases, is an &ldquo / Initial and Boundary Value Problem&rdquo / is reduced to a &ldquo / Two- Point or Multi-Point Boundary Value Problem&rdquo / by using the present &ldquo / Solution Technique&rdquo / . For this purpose, these &ldquo / Governing Equations&rdquo / are expressed in &ldquo / compact forms&rdquo / or &ldquo / state vector&rdquo / forms. These equations are numerically integrated by the so-called &ldquo / Modified Transfer Matrix Method (MTMM) (with Interpolation Polynomials)&rdquo / . In the numerical results, the mode shapes together with their corresponding non-dimensional natural frequencies are presented up to the sixth mode and for various sets of &ldquo / Boundary Conditions&rdquo / for each structural &ldquo / System&rdquo / . The effects of several important parameters on the natural frequencies of the aforementioned &ldquo / Systems&rdquo / are also investigated and are graphically presented for each &ldquo / Stiffened and Stiffened and Bonded Plate or Panel System&rdquo / . Additionally, in the case of the &ldquo / Bonded and Stiffened System&rdquo / , the significant effects of the &ldquo / adhesive material properties&rdquo / (i.e. the &ldquo / Hard&rdquo / adhesive and the &ldquo / Soft&rdquo / adhesive cases) on the dynamic response of the &ldquo / plate assembly&rdquo / are also presented.