An improved Fourier series method is presented for the free vibration analysis of the moderately thick laminated composite rectangular plate with general elastic supports and point supports resting on an elastic foundation. The approach is based on the first order shear deformation theory and foundation effect using two-parameter Pasternak foundation model. The displacement and rotation functions are generally sought, regardless of boundary conditions, as Fourier series and supplementary functions. All the series expansion coefficients are determined using the Rayleigh-Ritz technique. The excellent accuracy of the current results is validated by comparing them with existing results.