Steady flow regimes for three-dimensional lake-aquifer systems are studied via idealized mathematical models that are extensions of earlier simplified vertical section models of interaction between shallow lakes and underlying aquifers. The present models apply to a shallow circular lake at the surface of a rectangular aquifer of finite depth, yielding a truly three-dimensional representation of the resulting flow system. Flux boundary conditions are applied at the ends of the aquifer, with net vertical recharge or evapotranspiration at the water table. The lake is defined by a region with constant head. By determining and visualizing solutions to the discretized saturated flow equations, a range of possible flow regimes is identified, and their topological properties are studied. Tools for analyzing flow regimes are described, including a method for locating and mapping three-dimensional dividing surfaces within steady flow fields. Results show strong similarities between two- and three-dimensional systems, including a large number of flow-through, recharge, and discharge regimes and reverse flow cells. Flow lines calculated on a vertical plane through the middle of a lake resemble but are not identical to two-dimensional streamlines for a range of aquifer flow and recharge conditions. Estimates of the widths and depths of capture and release zones for various lake-aquifer geometries are asymptotic to earlier results for two-dimensional systems. Numerical predictions are compared with analytical results for certain limiting flow regimes. ¿ 2000 American Geophysical Union