An experimental and theoretical investigation is presented of farfield distortion of a finite‐amplitude wave generated by a circular‐piston source. Nearfield distortion is neglected. Thus the boundary condition is that the acoustic signal at the beginning of the farfield is a pure sine wave of amplitude proportional to the small‐signal directivity factor for the piston. The method of applying weak‐shock theory to obtain directivity patterns and propagation curves is outlined. A criterion for the maximum range at which weak‐shock theory is valid is derived for each harmonic. Anad hocmethod of matching at this range the small‐signal solution, with absorption included, to the weak‐shock solution is proposed. Data obtained for a fundamental frequency of 450 kHz and source levels of 109 and 127 dB (re1 μbar at 1 yd) are presented. Theoretical and experimental beam patterns are in good agreement. Propagation data presented for the 127‐dB source level are in poor agreement with the predictions of unmodified weak‐shock theory but in good agreement with the matched solution. In general, the experimental data support the hypothesis that harmonic generation in waves from directive sources may be described by specifying a boundary condition for each direction and then assuming that the distortion developing in that direction is not affected by distortion along any other direction.