A rigorous theory is developed for describing the diffraction of a plane wave by a doubly periodic array of annular apertures in a thick, perfectly conducting screen. Coaxial waveguide modes are used to describe the fields within each aperture, while the fields above and below the grid are written as plane wave expansions. Appropriate boundary conditions are applied at the upper and lower surfaces of the screen, and the method of moments is used to determine mode and wave amplitudes. Such a structure was found to exhibit excellent bandpass characteristics which can be adjusted by changing the size of the apertures and the thickness of the screen. >