A Ritz method using polynomial functions has been developed to analyse the vibration properties of composite laminate plates for boundary conditions that have not been analysed previously by means of such an approach. An investigation is made into the effect of ply orientation, orthotropic ratio and stacking sequence on the natural frequencies and mode shapes for different boundary conditions. The results are compared with finite element (FE) analysis and other analytical techniques. The results show a good agreement with the FE analysis and better convergence characteristics than other analytical methods.