This work is the examination of a cavity mode approach to the mode structure of a laser. Solutions of the vector wave equation for electromagnetic fields in and between perfectly conducting oblate spheroidal cavities are examined for the case of wavelengths much less than cavity dimensions. These solutions are the field modes in Fabry—Perot type resonators with equal‐radius concave spherical mirrors, or with concave—convex spherical mirrors, when the parameters of the oblate spheroids are chosen so that the radii of curvature and spacing on the axis of rotation match those of the resonator mirrors. Expressions for the transverse and longitudinal mode structures are derived. The eigenvalue equations are written, and are solved for the case of the two lowest‐order modes.