Recent WIND and GEOTAIL observations indicate that Alfv¿n waves can reverse their direction of propagation relative to the ambient magnetic field when they cross the bow shock [Sibeck et al., 1997>. To investigate this effect, we use three-dimensional magnetohydrodynamic (MHD) simulations to study an Alfv¿n wave (AW) propagating into the magnetosheath. Our results are consistent with the observations. The AW is set to propagate with a wave vector k pointing anti-sunward and largely opposite to the magnetic field direction, i.e. B⋅k<0. The interplanetary magnetic field (IMF) is given a typical Parker spiral angle. The primary Alfv¿n wave that is transmitted into the magnetosheath (AW') continues to propagate anti-sunward. In the dusk magnetosheath, AW' largely maintains this propagation direction through its entire passage through the magnetosheath. On the dawn side, however, AW' changes propagation direction relative to the magnetic field so that it propagates along the magnetic field instead of against it, i.e. B⋅k becomes positive. This effect is strongest in the region of the magnetosheath where field line draping forces the x component of the ambient IMF to change sign. The reversal of B⋅k is the end result of a phase shift between the velocity and magnetic field perturbations that occurs smoothly as the wave propagates toward the magnetopause. ¿ 1998 American Geophysical Union