The free-drift equations are solved for ice floes in a shallow sea of neutral stratification, typical of many high-latitude continental shelves. Solutions for ice drift and current velocity are obtained as a function of wind stress, ice thickness, and water depth. The ocean is modeled by second-order closure, which allows continuous solutions from 5 m total depth to deep water. Results are presented with drag coefficinets for the air/ice, ice/water, and water/bottom interfaces specified from recent surveys from the Bering Sea Shelf, a region with broad areas of water depths between 20 and 50 m. The solution shows little dependence on water depth for depths greater than 30 m. This occurs because turbulent mixing is a decreasing function of water depth and offsets other influences of finite depth. However, for water depths less than 30 m, ice velocities can charge rapidly with wind speed and water depth, and the presence of turbulence from tidal shear is very important for coupling wind-driven ice drift to the bottom. For the deep-water limit, the second-order closure solution confirms analytic solutions that indicate an increase of 20% in the ratio of ice speed to wind speed as the wind speed increases from 10 to 25 m/s.