An approximate method for computing the theoretical supersonic acoustic field from a plane piston, recently presented by the author and L. W. Labaw, is extended to cover a larger region and is applied to concave pistons as well. The resulting equations are given for a certain range of frequencies, piston sizes, and distances from the source. The excess acoustic pressure can be evaluated from them, along the beam axis and for a narrow region around it. It is shown that the assumed nature of vibration of the piston does not matter very much unless the source is sharply curved. The locus of maximum excess pressure is not, in general, near the center of curvature. Labaw's recently published data on the acoustic fields of curved crystals are analyzed in the light of the present equations. The agreement in general is satisfactory. However, it seems that his plane crystal was faulty or else that curved crystals must produce several times the acoustic intensity of plane ones with the same applied voltage.