Some properties of wave fronts or constant‐phase surfaces in the acoustic field of a piston‐like source are deduced from an approximate expression for the velocity potential. The calculations are limited to certain ranges of frequencies, piston sizes, and distances from the source, of chief interest in supersonics. The results comprise for plane pistons (a) a determination of the place where the wave fronts reverse their curvature from converging to diverging shape; (b) a calculation of the radius of curvature of the fronts at moderately large distances from the source; (c) an approximate theoretical equation for the shape of the wave fronts, which permits plotting the paraxial portion of these surfaces at medium and large distances. For a concave piston, calculations similar to those of (a) are made. A few comparisons with experimental results are given under (a), (b), and (c). Agreement is qualitative to semi‐quantitative.