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Fibers of noncircular cross sections are analyzed by a new algorithm based on the method of lines with discretization lines of unequal length. The material may have uniaxial anisotropy. The tangential field components have been matched at the noncircular interface of the structures. Results are shown for waveguides with elliptical and star-shaped cross section. To study the accuracy of the proposed algorithm, the results have been compared with other methods.