This paper deals with buckling and vibration analysis of initially stressed damped composite sandwich plates using assumed strain finite elements. A family of plate bending elements containing nine degrees of freedom per node are developed based on a refined higher-order shear deformation theory. The higher-order theory contains in-plane displacements that are expanded to include the higher-order terms in the Taylor series expansion as a result of which there is no need for shear correction factors. The popular assumed strain concept is used to ensure that the developed four- and nine-node elements pass the patch test and show no signs of shear locking and spurious zero energy modes in the present finite element formulations. Parametric studies are carried out to study the behavior of length to thickness ratios, boundary conditions, fiber orientations on vibration, and buckling of damped composite sandwich plates.