In this contribution a new and efficient integral equation formulation is presented for the analysis of arbitrarily shaped capacitive waveguide devices. The technique benefits from the symmetry of the structure in order to reduce the dimensions of the problem from three to two dimensions. For the first time, this technique formulates the waveguide capacitive discontinuity problem as a 2-D scattering problem with oblique incidence, combined with an efficient calculation of the parallel plate Green's functions. The numerical method allows the efficient evaluation of the electromagnetic fields inside the analyzed structures. Results for different practical capacitive waveguide devices are successfully compared with commercial software tools for validation of the proposed theory. Finally, a novel low-pass filter implementation based on circular conducting posts has been proposed. The field contour lines in the critical gaps of the new structure are curved due to the use of rounded posts. This could result in improved power handling capabilities with respect to standard corrugated low-pass filters.