A semianalytic method is presented that can be used to calculate the acoustic radiation in a domain exterior to a source that is vibrating harmonically in time. This method follows the traditional technique of an expansion of the boundary conditions in an infinite series of eigenfunctions and of a least‐squares approximation of this expansion by a finite series of the same functions. For simply connected bodies, such as a finite cylinder, that are not constant coordinate surfaces and for which a complete set of geometrically appropriate eigenfunctions is unavailable, the spherical eigenfunctions are employed as the complete set of eigenfunctions. Farfield patterns produced by radially pulsating cylinders of length equal to twice the diameter have been calculated for ka = 1,2, and 5 and are compared to the calculated farfield patterns of the physically similar situations of a finite‐length line source and a radially pulsating band of finite length on an otherwise inert, infinite cylinder. In addition, the ...