Exact solutions for the interaction between two concentric cylindrical waves and between two concentric spherical waves are presented. The scattered‐pressure amplitude in the far field is shown to be constant in the cylindrical case and to be proportional tor−1lnrin the spherical case, whereris the distance to the source of primary waves.A near‐field solution is derived for the scattered waves generated when two sharply defined, plane‐wave beams of square cross section intersect at right angles. A comparison is made of the theory with recent experiments in which beams of circular cross section were used. It is concluded that if the scattered waves do exist, their amplitudes are at least 40 dB below those that are predicted by this theory.When a hard object is placed in the region of intersection, scattered waves are observed. This effect can be explained by the fact that with the addition of the hard object (a cylinder) the primary waves have components of the same symmetry. These components are the waves scattered from the primary beams by the object. Evidence is presented to show that these components, having the same symmetry, interact strongly in the volume surrounding the object.