A combined method, using the finiteelement approach and the analytical approach, is described for the solution of arbitrarily shaped discontinuities in a dielectric slab waveguide. Both TE and TM mode incidences are treated. The method is based on replacing the unbounded configuration by a corresponding bounded structure. The validity of the method is confirmed by comparing numerical results for step discontinuities with other available results. Computed results are also presented for typical boundary deformations in optical fibres caused by a fusion splice.