The effect of air loading on the normal modes of a vibrating membrane may be systematically calculated by making use of the relevant Green's functions for the air medium. Formal and numerical results have been obtained for the case of rectangular membranes with and without rectangular‐box and split‐cylinder air enclosures, and of circular membranes with and without cylindrical and hemispherical air enclosures. Our analysis may be used to assess the relative importance of bowl shape, enclosed‐air loading, and outside‐air loading on the normal modes of the kettledrum.