The transfer of energy from the magnetosphere to the ionosphere occurs through complex mechanisms that often involve shear Alfv¿n waves, implying that the interaction of these waves with the ionosphere is fundamental to our understanding of the coupling process. Indeed, a variety of problems that involve magnetosphere-ionosphere coupling assume that the ionosphere acts as a perfectly reflecting boundary, although we know that this is not the case in general. In this work, we calculate the reflection coefficient of shear Alfv¿n waves incident on the ionosphere under three different ionospheric profiles. Our results indicate that 1) under all profiles considered, reflection of shear Alfv¿n waves with perpendicular lengths of ~1 km or less is negligible and 2) under a profile that might be typical of a nightside ionosphere, reflection of shear Alfv¿n waves is significant only for waves with frequencies below ~0.4 Hz and &lgr;x above ~2 km; reflection of waves with &lgr;x less than ~2 km is poor. ¿ 2001 American Geophysical Union