The propagation of acoustic waves from a high‐frequency line source in a two‐dimensional parallel shear flow adjacent to a rigid wall is analyzed by a ray method. The leading term in the resulting expansion is equivalent to the geometrical acoustics theory of classical wave propagation. It is shown that energy from the source is radiated either directly to the farfield, or by first reflecting from the wall. In addition, energy is trapped in a channel adjacent to the wall and downstream from the source. The rays in this channel form an infinite sequence of caustics progressing downstream. Since the geometrical acoustics approximation is invalid on and near caustics, a boundary layer method is employed to determine the acoustic fields near the caustics. It is shown that the amplitude of the fields on and near the caustics isk2/3larger than the geometrical acoustics field for largek. Herekis a dimensionless wavenumber of the source. Moreover, the vorticity of the acoustic fields in the caustic regions isk7/6larger than the geometrical acoustics field. The possible significance of these results for vehicle self‐noise and the formation of turbulent spots in the sublayer of a turbulent boundary layer is discussed.