A numerical model is developed to simulate currents generated by hurricanes on the outer continental self and slope. Emphasis is on the mixed-layer response within a few hours of storm passage; however, some attention is given to the lower layer and shelf wave responses. The model is based on a layered, explicit, finite difference formulation using the nonlinear primitive equations including conservation of heat. The problem of topography intersecting the model layer is resolved by introducing artificial steps of the order of 100 m where the layer intersects the slope. Model comparisons are presented for three Gulf of Mexico hurricanes using a 0.2¿ grid. For two of the storms, the model reproduces better than 80% of the observed velocity variance with correlation coefficients of greater than 0.8 for the mixed layer. Discrepancies in the comparisons are traced to unresolved local topography and nonstorm forcing such as warm-core rings. Futher model simulations reveal that (1) substantial shelf waves were generated with phase speeds of 4 to 10 m s-1, (2) the response is primarily baroclinic even in water as shallow as 200 m, (3) an entrainment law which scales with the velocity difference between the mixed layer and upper thermocline yields markedly better comparisons than one which scales with the wind stress, and (4) deviations from a straight-line storm path can significantly alter the response. ¿ American Geophysical Union 1989