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In order to describe the main features of the first modes of a self-focusing parallel plate waveguide laser, a numerical method based on a high-frequency formal asymptotic expansion has been developed, which is able to give both the shape of the first modes and the associated losses. In the planar and circular geometry, the method was shown to give the same results as the analytic calculation. A good agreement with experimental results was found in the case of a parallel plate self-focusing waveguide. In this case, examples of numerical results are given for various curvature radii and spacings of the plates.