Abstract: The dispersion relation of the rectangle waveguides with corrugations was mathematically modeled and theoretically analyzed.The original work was that the electromagnetic(EM) fields were precisely described as the superposition of infinite spatial harmonic-waves in the rectangle waveguides,and infinite standing-waves in the corrugations,respectively.First,at all the interfaces,the system with infinite equations was derived by means of specific boundary-matching conditions; second,the equation system was numerically solved by truncation of the infinite series; and finally,the EM-field distributions and dispersion characteristics were theoretically calculated.The new model outperforms the conventional one because the superposition of infinite standing-waves in the corrugations is closer to the realistic situation.The results calculated with the newly-developed model were in good agreement with those simulated with CST microwave studio code.