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Six charts are given which may be used for designing cylindrical resonant cavities whose cross sections are circles, concentric circles, squares, or rectangles. A new method of representing multiple-resonance phenomena is used, to which the name "mode lattice" has been given. The mode lattice is an alignment chart which relates the size and shape of a cavity with resonant wavelength for a large number of modes. Points distributed on a lattice represent the modes. The equations involved, the method of use, and the special advantages of each chart are described, together with the method of construction. A set of equations has been derived for calculating the effect of small changes in dimensions or wavelength for resonators of all the above shapes.