Exact method for modal analysis of plates with arbitrary boundary conditions.Enhancement of the Wittrick-Williams algorithm by resolving the J0 count elegantly.Securing exact solutions for free vibration of plates for benchmark purposes.The method has two orders of magnitude higher computational efficiency than the FEM.Discussion and conclusions on a wide range of existing analytical and exact methods. An exact method for free vibration analysis of plates with arbitrary boundary conditions is presented. This is achieved by integrating the spectral method into the classical dynamic stiffness method. The formulation satisfies the governing differential equation exactly and any arbitrary boundary conditions are satisfied in a series sense. The Wittrick-Williams algorithm is enhanced with several elegant techniques to obtain solutions. The exactness and computational efficiency of the method are demonstrated by comparing results obtained from other methods. Finally, mathematical and physical insights are gained and significant conclusions are drawn for various analytical methods for free vibration analysis of plates.