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SUMMARYThe convergence proof of plate eigenvalue solutions from conforming displacement finite elements is presented. The analysis is based on converting a thick plate free vibration problem into a corresponding isoperimetric variational problem. A conforming thick plate element is used to illustrate the mathematical development. On the basis of the derived asymptotic rate of convergence of the approximate eigenvalues, the authors propose a practical method of improving the numerical solutions. Extension of the mathematical proof to cover classical thin plate finite elements is briefly discussed.