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Degenerate scale occurs once the boundary integral equation(BIE)is employedto solve plate problems.There are two ways to be considered.First,the degenerate kernel for expressing the closed-form fundamental solution is utilized to study the occurring mechanism for circular and elliptical plates using polar and elliptical coordinates,respectively.Second,the BIE is discretized andreformulated to a 4 by 4 eigenproblem to obtain degenerate scales instead of the direct-searchingscheme.Analytical degenerate scales for the circular and elliptical shapes are obtained while numerical results for general shapes are also considered.