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A mode-matching technique combined with Galerkin's method is proposed in this paper to analyze the characteristics of striplines embedded in an inhomogeneous cylindrical medium. The potential in each layer is expressed in terms of eigenmodes obtained numerically. Coupling between two sets of eigenmodes in contiguous layers is described by defining potential ratio coefficient matrices. An integral equation is derived based on these eigenmodes with charge on the stripline as unknown. The method of moments is then applied to solve this integral equation. Various parameters are analyzed for their effects on transmission characteristics.