A one-phase, two-dimensional fluid model is applied to predict the flow and thermal fields between electrodes in an electrochemical drilling (ECD) process. A body-fitted curvilinear coordinate transformation is used such that a moving, irregular surface of the workpiece in the physical domain becomes a fixed, regular boundary in the computational domain. The equilibrium workpiece shapes predicted by the present model agree in general with experimental results. Results show that some transport properties vary abruptly in the transition region. In the transition region, the rate of change of pressure in the streamwise direction is higher near the tool than near the workpiece. The electrolyte temperature near the surfaces of the workpiece and the tool in the transition and side regions is higher than that in other places.