Observations in the Greenland Sea marginal ice zone suggest that when strong stratification occurs near the surface, momentum flux into the internal wave field of the upper ocean can be a major component of the force balance that governs ice drift. Since energy is radiated away by the internal waves, turbulent mixing and heat flux are also affected. We investigate the downward flux of momentum and energy by internal waves in an ice-covered ocean, with an idealized model comprising a mixed layer overlying a deep, uniformly stratified layer. A buoyancy jump separates the mixed layer from the pycnocline. Drag from a single wave number component of the under-ice roughness spectrum is derived as the product of a drag coefficient (based on ice speed, under-ice roughness wave number and amplitude, and uniform stratification to the ice-ocean interface) times an attenuation factor that depends additionally on mixed-layer depth and the buoyancy jump at the base of the mixed layer. The model is extended to a plausible spectrum of under-ice roughness by integration over wave number space. Internal wave effects are parameterized in terms of the drag coefficient from the integrated spectrum and incorporated into an upper ocean turbulence model. Model calculations show that plausible values for the peak wave number of the idealized spectrum and roughness variance can account for (1) decreased ice velocity relative to the wind, (2) decreased heat exchange coefficient between the ice and ocean, and (3) lack of mixed-layer deepening, all of which were observed during the last week of the 1984 Marginal Ice Zone Experiment. ¿ American Geophysical Union 1989