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A study on the free-vibration analysis of plates and shells is described in this paper. In order to determine the natural frequencies of plates and shells, a nine-node degenerated shell element is developed by using the degenerated solid concept based on Reissner–Mindlin (RM) assumptions which allow the shear deformation and rotatory effect to be considered. All terms required in the shell finite element (FE) formulation are defined in the natural domain. In particular, assumed natural strains are derived to alleviate the locking phenomena inherited in the RM shell elements. The natural constitutive equation is used in conjunction with the natural strain terms. The proposed shell FE formulation offers significant implementation advantages since it consistently uses the natural co-ordinate system. Various numerical examples are carried out and its results are then compared with the existing exact solutions and the numerical solutions calculated by other shell FEs.