<p>We have developed a method for calculating modes in axially symmetric open cavity resonators. The method is based on a weak formulation of the equations of electrodynamics, a finite element method, and a perfectly matched layer method for limitation of the computational domain. Using a “non-canonical” echelette cavity as an example, TE modes are simulated. It is shown that such a cavity has groups of longitudinal modes whose properties are similar to those of the longitudinal modes in “classical” cavities, which have the form of weakly nonuniform cylindrical waveguides loaded on both sides with tapering and expanding horns. The frequencies and the diffraction and ohmic Q-factors of the echelette-cavity modes are calculated. It is found that the ohmic Q-factor significantly exceeds the diffraction Q-factor, which agrees qualitatively with the results presented in the literature. It is shown that there exist optimal values of the corrugation radius and amplitude, at which the diffraction Q-factor is maximum.</p>