Spheroidal coordinates and wave functions are used to analyze the sound radiation from a prolate spheroid whose surface vibrates in an arbitrary pattern. Expressions are derived for the pressure distribution, velocity amplitude, radiation impedance, and directivity factor in each spheroidal radiation mode. Numerical results are derived for two special examples: (1) a rigid‐body vibration of a thin spheroid, and (2) an “accordion‐like” vibration of a thin spheroid.