The self‐acoustic radiation impedance of cap‐shaped and ring‐shaped pistons conformal to a rigid prolate spheroidal baffle and vibrating with uniform normal velocity is calculated using prolate spheroidal wave functions. The necessary spheroidal functions are obtained using recently developedFORTRANcomputer programs. Plots of the normalized radiation resistance and the normalized radiation reactance as functions of the acoustic size parameterhare presented for several different baffle shapes and relative piston sizes. The effect of the baffle size and curvature on the radiation impedance is shown to be small.