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This letter presents an extension of the discrete mode matching method to the analysis of dielectric waveguides with noncircular cross sections. The problem is analyzed in cylindrical coordinates expanding the fields in terms of Bessel functions. Matching of the fields tangential to the interfaces between different dielectric layers is ensured by applying the proper boundary conditions. The mathematical formulation is given in this letter, followed by its application to compute the propagation constants in elliptical dielectric waveguides.