When oceanic internal waves are forced by rapidly translating winds and wind stress is applied as a body force which is uniform within and vanishes outside a surface layer, their spectrum has a vertical wave number indistinguishable from the Garrett and Munk observational synthesis. Bandwidth and high-wave number dependence are functions of the stress gradient layer thickness and vertical structure. The close correspondence between the predicted spectrum of forced waves and observed spectra suggests that the wave number shape of the near-inertial part of the oceanic internal wave spectrum is a consequence of wind forcing. The same mechanism is consistent with equatorial wave number spectra. Conversely, if mid-latitude near-inertial waves and equatorial waves are directly wind forced, then their observed wave number spectra imply that the vertical gradient of stress due to wind is nearly a step function which cuts off sharply at a depth comparable to observed seasonal pycnocline depths. ¿ American Geophysical Union 1988