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A coupled finite boundary element method (CFBM) solution is developed for the EM fields scattered by an arbitrary multiple-dielectric coated conducting cylinder. The field in the dielectric coating domain is formulated by the finite element method, while the radiation condition is included by adopting a boundary element method. Numerical results show that the CFBM does not suffer from non-uniqueness in the resonance frequency. An excellent agreement between CFBM solutions and extract solutions for coated circular cylinders is observed.