The existence of Rayleigh scattering of elastic plane waves by anisotropic homogeneous inclusions is theoretically demonstrated. The case of transverse isotropy is studied in detail. It is shown that a scattered longitudinal wave creates radial‐longitudinal (P), collatitudinal‐shear (SV), and azimuthal shear waves (SH). Likewise, scatteredSVandSHwaves, each generate radialPwaves andSVandSHshear waves. All scattered amplitudes are proportional to the square of the frequency and have radiation pattern signatures as those of equivalent dipoles, center of compression, and double couples. It is shown that observations of spatial patterns of scattered amplitudes can yield, through inversion, the elastic constants of the anisotropic inclusion. The results obtained can serve as a theoretical basis for the observed short‐periodSHandSVwaves from underground explosions at teleseismic distances.