Diffraction of short acoustic waves (plane or otherwise) may be treated by methods akin to geometrical optics provided that the lateral dimensions of the diffracting obstacle are large as compared with a wavelength. On the other hand, it is possible to construct thin- or slender-body theories that are directly analogous to corresponding aerodynamic theories only if the wavelength is large as compared with the lateral dimensions. The present theory is an attempt to explore the hazy middle ground where the wavelength and lateral dimensions are comparably small. Diffraction of a plane wave by a two-dimensional thin wing at zero incidence to the oncoming wave is considered as a model for this class of problems, and a method is given for finding the scattering into the region near the plane of the wing. In particular, we find a 45° phase shift and an asymptotic “x−3/2” decay of the scattered disturbance in the shadow region directly behind the wing. A corresponding result for a slender, sharply pointed, three-dimensional obstacle indicates a 90° phase shift and an “x−2” decay with distance.