After a brief introduction, the wave equation for a membrane in rectangular coordinates is derived. Next comes the solutions in rectangular and polar coordinates together with the Green's function. The membrane and free space wave equations are solved simultaneously to model a circular electrostatic loudspeaker radiating into free space. The solution of the plate wave equation in polar coordinates, together with the Green's function, follows and various edge boundary conditions are applied to a circular plate. In each case the eigenvalues are calculated and the eigenfunctions plotted. The shallow spherical shell is treated in a similar way to the plate initially but the boundary conditions are representative of an actual dome-shaped loudspeaker diaphragm with a compliant edge suspension and coil mass. The shell and free space wave equations are solved simultaneously to model sound radiation from a loudspeaker in an infinite baffle. The effect of varying the dome height is explored. The chapter concludes with a model of a novel induction loudspeaker in an infinite baffle. This exploits the phenomenon whereby a circular free plate excited by a point force at its center radiates has a flat on-axis response and radiates constant power at all frequencies.