The work is devoted to the calculation of the open ring resonators with astigmatic reflecting surfaces. To solve this problem, the standard Fox and Lee method has been modified. Using it, the mathematical models of the distribution of the electric field strength of the ring resonators were constructed and tested. In particular, the behavior of the electric field strength vector in a resonator composed of four toroidal-shaped reflecting surfaces was calculated. Also, such an approach allows calculating diffraction losses in ring resonators with astigmatic reflecting surfaces and analyzing the effect of the misalignment of their elements.