Abstract Sandwich plates and cylindrical shells composed of two composite laminated faces and an ideally orthotropic elastic core are considered in this paper. Since the natural frequencies of sandwich structures may not be affected by the accuracy of local behaviors, to avoid the complexity involved in the higher-order shear deformation theory and layerwise theory and to supplement the loss of the transverse shear deformation in the classical lamination theory, a modified first-order shear deformation theory was employed to obtain the closed-form solutions of natural frequencies of certain particular problems of sandwich plates and shells such as a rectangular composite sandwich plate with symmetric cross-ply laminates with all edges simply supported. Mathematical formulation extended by the classical methods used in isotropic thin plates was also established to deal with the general cases of sandwich plates and cylindrical shells. Numerical results show that the solutions obtained by the present methods are accurate enough to serve as a quick check for the other numerical solutions.