This paper presents a method for the dynamic analysis of a thin, elastic, isotropic rectangular plate. The method is a hybrid of finite element theory and classical thin plate theory. The displacement functions are derived from Sanders' thin-shell equations, and are expanded in power series. Expressions for mass and stiffness are determined by precise analytical integration. The free vibrations of rectangular plates, with various boundary conditions, are studied by following this method. The results obtained reveal that the frequencies calculated in this way are in good agreement with those obtained by others.