Past seismic investigations have relied principally on analysis of first arrival P waves with longitudinal particle displacements rather than the slower shear waves with more complicated transverse motions. Consequently, event quite elementary behavior of shear waves is sometimes poorly understood. It might be supposed, that the direction of polarization of shear waves would remain essentially unchanged on reflection from a plane horizontal isotropic-to-isotropic interface. This paper shows that in general this is not the case. In some circumstances, the direction of polarization can rotate by almost 180¿ as the angle of incidence varies. Since there is growing interest in using shear wave polarizations to examine the internal (anisotropic) structure of the rockmass in both earthquake and exploration seismology, such anomalous behavior of shear wave polarizations is important for understanding the behavior of shear waves and investigating the structure of the crust. The anomalies we display are a necessary result of the behavior of the reflection coefficients, which are well-known, but the possibility of such wide variations in polarization of the reflected shear wave does not appear to have been recognized previously in the literature. ¿ American Geophysical Union 1990