In the present work, a modified higher-order shear deformation theory is developed to analyze isotropic and composite plates to obtain the static response as well as dynamic characteristics using Ritz solution technique. The displacement-field equations of Lo's higher order shear deformation theory are modified by representing the total rotation of the normal to the mid-plane by two components, bending and shear rotations. The model is valid for thin and thick plates. The plates are subjected to mechanical loads with different types of boundary conditions. A Mathematica code is developed to analyze different plate problems. The obtained results are compared to the available studies solved by different theories and finite element methods. It is shown that the obtained results are accurate using less number of degrees of freedom.