The theory of the scattering of plane waves of sound by isotropic circular cylinders and spheres is extended to take into account the shear waves which can exist (in addition to compressional waves) in scatterers of solid material. The results can be expressed in terms of scattering functions already tabulated. Scattering patterns computed on the basis of the theory are shown to be in good agreement with experimental measurements of the distribution‐in‐angle of sound scattered in water by metal cylinders. Rapid changes with frequency in the distribution‐in‐angle of the scattered sound and in the total scattered energy are found to occur near frequencies of normal modes of free vibration of the scattering body.