The modal low frequency noise generated by a vibrating elastically supported circular plate embedded into a flat infinite baffle has been examined. The main aim of this study is the analysis of the radiation efficiency. Low frequency approximated formulas have been presented. They are valid for all the limiting boundary conditions of the plate with its edge clamped, guided, simply supported or free as well as for all the intermediate axisymmetric boundary configurations. The formulas are expressed in the elementary form, useful for numerical computations. They are a generalization of some earlier published results. First, they are valid for axisymmetric and asymmetric modes since both kinds of modes play an important role in the low frequency range. Second, a single formula for the radiation efficiency, valid for all the axisymmetric boundary configurations, has been proposed. A numerical example for the sound power radiation has been given for some hatchway covers mounted on a ship deck.