In this paper, the free vibration of thick, isotropic and laminated composite rectangular plates with point supports is analyzed by the ยฎnite layer method. A new set of two-dimensional basic functions, which satisยฎes the kinematic boundary conditions at the edges of the plate and the zero-displacement conditions at point supports, is developed to describe the variation of three-dimensional displacements in the plane of a thin ยฎnite layer. Onedimensional linear or quadratic shape functions are adopted to describe the variation of the displacements through the thickness layer. The governing eigenvalue equation of the plate is derived via the conventional displacement method. Numerical results for the three-dimensional vibration of rectangular plates with point supports are presented herein for the ยฎrst time. The eigenfrequencies of simply-supported rectangular plates with a central pointsupport are studied in detail by considering the variations of aspect ratio, side-to-thickness ratio, properties of materials, number of laminates and stacking sequences. Comparison with known thin-plate and Mindlin-plate solutions is carried out to verify the applicability and accuracy of the proposed method.