A review of theories concerning the propagation of internal gravity waves in a horizontally uniform shear flow concludes that an upward transport of horizontal momentum inevitably accompanies the generation of such waves in the atmosphere, the mean flow being affected only at precisely those levels where the waves are dissipated. If the mean wind depends on horizontal position there may be a continuous transfer of momentum from the waves to the mean flow during propagation. In the absence of intense clear air turbulence or a critical level where the intrinsic frequency vanishes, many waves propagate upwards to great heights, even if the mean wind is time dependent. Computations of the wave drag in a 19 m s−1 gradient wind over hilly terrain in north Wales show that on that occasion it amounted to 4 dyne cm−2, of which 3 dyne cm−2 probably acted on the atmosphere above 20 km. Copyright © 1969 Royal Meteorological Society