Abstract: For open cavities with slowly varying cross-section the reflective coefficient of diffraction under general nnsymmetrical mode, when "a phase correction factor" is introduced, can be found by use of the method of transverse-section. Parameters of the open cavities are found under resonant conditions of longitudinal wavenumber. The method described can be used to solve multi-mode problems. Several different types of open cavities are studied, and it is concluded that coaxial open cavity with varying section has the most sparse eigen spectrum. In this paper, method of engineering design is briefly discussed.