nine-node isoparametric plate bending element is used in this paper for free vibration analysis of isotropic and laminated composite plates on elastic support. The Mindlin’s First-Order Shear Deformation Theory (FSDT) is incorporated in the finite element formulation. The elastic springs are arranged at various points under the plate with different boundary condition. The element stiffness matrix is obtained using the principle of virtual work, and the stiffness of the springs is added to the element stiffness matrix to obtain the overall stiffness matrix of the plate. Free vibration analysis of plate with different side ratios (a/b), thickness ratios (a/h), fibre angle orientation and boundary conditions have been analysed in this paper. Present finite element results have been compared with established results, and some new results have been presented which will be useful for further research in this field.