In this paper, we determine the different possible couplings at the discontinuities of the two circular and rectangular waveguides using the trapez-method. The development of the normal modes of the fields allows us to obtain the amplitude of the fields of the transverse electric (TE) and magnetic (TM) modes. The calculation of the coupling integrals allows us to obtain the coupling matrices and to verify if the coupling is possible or not between the modes of these two waveguides.