Abstract: Based on Reissner-Mindlin first-order shear deformation plate theory, the free vibration analysis of an initially stressed, moderately thick rectangular plate with point supports is presented. The initial stresses are induced by in-plane mechanical loads or temperature field, which is assumed to be a uniform distribution over the plate surface and a linear through-the-thickness temperature gradient. A set of Timoshenko beam eigenfunctions, which satisfies different kinds of geometric boundary conditions, is adopted and Rayleigh-Ritz method is employed to determine the natural frequencies of the plate. Numerical results are given in tabular forms, showing the effects of locations of points, boundary conditions and transverse shear deformation on the vibration characteristics of the plate. The results reveal that the frequencies are reduced by increasing temperature and initial compressive loads.