A class of non uniform dielectric waveguides with arbitrarily transverse cross sections was analyzed by a method, which combines the staircase approximation with the edge element and mode matching procedure.Non uniform constituent regions were approximated by cascaded step discontimuities. Multi mode microwave networks was introduced to represent the step discontinuities. After the eigenvalue problem of the local waveguide was solved by the edge element method, the scattering parameters of these microwave networks were calculated with mode matching method. The transmission property of the whole non uniform structure then was obtained by the treatment of the cascaded microwave network. Because of the versatility of edge element method, the present approach can be used to analyze non uniform dielectric waveguides with different transverse cross sections.