Two versions of a {1, 2} higher order laminate plate theory are derived for elastodynamics and used to compute natural frequencies and mode shapes for homogeneous and laminated plates. The theories include deformations due to transverse shear and transverse normal stretching and account for rotary and thickness-motion inertia. Analytic natural frequencies and mode shapes are obtained for thin and thick orthotropic and laminated simply supported plates and compared with exact solutions of three-dimensional elasticity, the higher and first order shear-deformable theories, and the classical laminate plate theory. Both versions of the present theory are shown to provide improved accuracy over other approximate theories when compared to elasticity theory, particularly for thick laminates and high frequency modes. The theory also accurately predicts the lowest thickness-stretch frequencies which cannot be obtained with first order shear-deformable theories. From the computational perspective, the theory is especially well-suited for generating simple and efficient displacement finite elements based on conventional C 0 -continuous displacements and five degrees of freedom at each boundary node. An approximation scheme for a three-noded triangular plate element is also discussed, together with a numerical study demonstrating the element performance in relation to two commercial plate elements.