Abstract The development of new mathematical model for guide polarization converter with diaphragms was carried out in the research by the method of wave matrices. In addition, numerical modeling of the performance of a polarizer with diaphragms is made by simulating the propagation of the fundamental modes with perpendicular linear polarizations. The wave matrix model was obtained by splitting the polarizer into separate structural elements. Each element was described by its own wave transmission matrices. As a result, a general wave scattering matrix was formed. Based on the elements this matrix the electromagnetic characteristics of the considered polarizer were obtained theoretically. In particular, complex reflection and transmission coefficients were calculated. Their modules and phases were analyzed in the frequency interval 10.7-12.8 GHz. To check the correctness of the obtained results an independent numerical simulation was carried out applying the finite element methodology in the frequency interval. The results of both approaches are in good agreement. The engineered converter of polarization with four diaphragms provides a reflection coefficient modulus of less than 0.14 and a transfer coefficient modulus of more than 0.99 for two orthogonal types of polarizations. As a result, a rigorous mathematical method was developed to analyze the elements of the scattering matrix of a waveguide polarizer with diaphragms. It can be used for the development of new broadband waveguide polarizers and waveguide filters based on diaphragm elements.