SUMMARYIn this paper we present a new theoretical model for the modelling of the microstrip line as well as two types of discontinuities: regular (open end, step, bend and T-and cross-junctions) and irregular (stub and bent-stub). The two-dimensional exact dyadic Green function of a grounded dielectric slab has been used with the Galerkin's technique. The subdivision of the discontinuity in a network of juxtaposed unit cells, characterized by their own longitudinal and transversal current distributions, allowed the treatment of a large class of irregular discontinuities in addition to the regular discontinuities. The obtained results have been commented and compared with those of different approaches and with experimental results where a good concordance has been observed.