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In this paper, a new method to efficiently analyze substrate integrated waveguide (SIW) based devices with multiple accessing ports is presented. The problem is considered as a 2-D electromagnetic problem assuming no field variation normal to the dielectric substrate. The incident and scattered fields from each circular cylinder are expanded with cylindrical modes, and the fields in the waveguide ports are expanded using progressive and regressive modal summations. The addition theorems of Bessel and Hankel functions are used to analyze the full-wave behavior of the SIW device. In order to extract the circuital parameters, the hybrid mode-matching between guided and cylindrical modes is done by projecting continuity equations in a circular boundary containing the whole SIW structure over the inner modes of each region. Applying this new technique, it is possible to analyze multiple port devices by solving a set of integrals that can be easily approached analytically or by using the inverse fast Fourier transform, avoiding the use of non efficient numerical methods. It is shown that the new method runs faster than commercial software packages and other techniques recently published.