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An algorithm is presented to compute the scattered field in anisotropic media, using finite differences (FD) applied to grid points on a cylindrical unconstrained triangular mesh, illuminated by obliquely incident plane waves. The material boundaries and electromagnetic characteristics are prescribed in x-y coordinates only, independent of z. The permittivity and permeability are tensors, with non-zero xy and yx elements, and with each element also independent of z. The ability to analyze arbitrarily polarized waves incident from any direction in space gives the proposed method an advantage over previously reported techniques of computing the fields in the presence of anisotropy.