The method derived in Part I for investigating the propagation of weakly nonlinear acoustic waves in systems described by curvilinear coordinates is extended herein to a three‐dimesnional situation. Specifically, this is a determination of a uniformly valid first order approximation to the waves radiating from an infinitely long cylinder vibrating harmonically in a mode having circumferential wave numbernand axial wavelengthL. The phenomenon of self‐refraction, in which the rays, as well as the wavefronts, are distorted by the wave motion, is shown to be the explanation for some unexpected types of distortion in the profiles of the pressure and velocity component waves. An important development is the disclosure that the three‐dimensional case of large, but finite,Lcannot be used to deduce the response in the two‐dimensional case of infiniteLstudied in Part I. The explanation of this situation is found to lie in the existence of a dispersion relation for the phase velocity of linear waves in the three‐dimensional case.