This paper presents new simple analytical technique for the development and optimization of polarizers based on a square waveguide with irises. The presented technique applies scattering and transmission matrices of the structure elements for the calculation of general scattering matrix of the whole polarizer. For two types of fundamental modes polarizations the irises are simulated as inductances or capacitances, which are connected in parallel into the equivalent transmission line. In order to check the performance of developed simple analytical technique the polarization and matching characteristics of a square waveguide polarizer with two irises were calculated theoretically. The investigation of the influence of the iris parameters on the electromagnetic characteristics of the polarizer has been performed in the paper. In the operating frequency band 7.4-8.5 GHz the optimized design of a square waveguide polarizer with two irises provides voltage standing wave ratio less than 2.8 for both polarizations. Differential phase shift of the polarizer is 90° ±8°. Axial ratio is less than 1.6 dB. Corresponding crosspolar discrimination is higher than 21.7 dB. Therefore, developed new simple analytical technique for the calculation of iris polarizer characteristics can be widely used for the approximate estimation of their performance. The subsequent optimization of the design must be carried out with the account of higher order modes or using accurate numerical simulation.