Most investigations of the sound field of a moving source deal only with point sources. We have examined the sound field of finite sources, moving with constant velocity. The simplest possible vibrators have been chosen,viz., a pulsating circular cylinder and a pulsating sphere. The solution is an infinite series in terms of Mathieu functions in the two‐dimensional case, and in terms of prolate ellipsoidal functions in the three‐dimensional case. Besides the rigorous solutions, asymptotic formulas valid for large distances away from the source are given.