The modern approaches to the numerical analysis of resonators of coaxial gyrotrons are considered in the article. These devices are used for plasma heating, generation of entrainment currents, and in other purposes in devices of controlled nuclear fusion with magnetic retention. The singular integral equation has been obtained and two discrete mathematical models for its solution have been built. The constructed approach has been compared with the simplified impedance model. The algorithm for calculation of ohmic losses in the inner corrugated conductor has been described.