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Using far from cutoff approximation (2a0 ≫ 1) we have derived elegant expressions for the characteristic equations and their relevant solutions to determine the guided wave features of an optical waveguide having an axial dielectric anisotropy. Also, the attenuation constant has been calculated following the concept of a complex permittivity in a lossy medium. For TE and TM, as well as hybrid modes studied here, the results computed by the approximate method show very good agreement with those of the exact analytical solutions. The dependence of the power carrying capacity and attenuation on the waveguide parameters highlights the usefulness of the dielectric anisotropy in optical waveguides.