In this paper, the fundamental theory of FTER-Q switch resonator is developed. The resonator is composed of many optical elements, it cannot be solved by the conventional method. Combining matrix optics with integral equations of diffractions of optical resonator, we obtain a theoretical solution, which gives out a lot of quantities, such as Fre-snel number, diffration losses, resonace frequency and its interval, etc., that can be compared with the result of parallel plane resonator.