Abstract: Geometric acoustics, or acoustic ray theory, is used to analyze the scattering of high-amplitude acoustic waves incident upon rigid circular cylinders. Theoretical predictions of the nonlinear evolution of the scattered wave field are provided, as well as measures of the importance of accounting for nonlinearity. An analysis of scattering by many cylinders is also provided, though the effects of multiple scattering are not considered. Provided the characteristic nonlinear distortion length is much larger than a cylinder radius, the nonlinear evolution of the incident wave is shown to be of much greater importance to the overall evolution than the nonlinear evolution of the individual scattered waves.