This problem is a natural continuation of the works of Morse on the rigid piston in a rigid spherical housing. Its solution is made possible by the little known but widely applicable method of Botman. A free circular disk driven at its center is assumed as the dynamic model. The method of Kirchhoff as given by Rayleigh is used to find the values ofkafor the first two axisymmetric modes. These together with the rigid piston mode give an adequate representation for the range ofkaof interest (ka<8). Botman's method is used in conjunction with an IBM 7090 computer. Machine limitations dictated the use of only 10 spherical harmonics: close fits to vibrational modes were not possible in spite of the choice of θ = 30° for the angle subtended by the piston. No significant error in the integrated radiation reaction is expected, however,owing to the cutoff properties of spherical wave impedances. Computed graphs ofX,R, directivity, and source level with comparison to Morse's results are given. Computed patterns are also shown. Some inferences with regard to the design of practical underwater radiators characterized by wide frequency range and omnidirectional patterns are made.