The alluvial aquifer at Louisville, Ky., lies in a valley eroded by glacial meltwater that was later partly filled with outwash sand and gravel deposits. The aquifer is primarily unconfined, and the direction of flow is from the adjacent limestone and shale valley wall toward the Ohio River and major pumping centers. Pumpage and water-level data indicate that the alluvial aquifer was in a steady-state condition in November 1962 and again in November 1983. Between these two dates, water-level data indicate a general rise in the water table. A two-dimensional finite-element ground-water-flow model of the alluvial aquifer was calibrated for both the steady-state and the transient-state period of 1962-83. The year 1962 represented a period in time when pumping was nearly three times that in 1983. The simulated steady-state water budget for 1962 indicated that of the total recharge to the aquifer of 5.19 million feet per day, 37.2 percent was flow from the river to pumped wells, 28.3 percent was recharge from rainfall, 19.7 percent was flow across the eastern valley wall, and 14.8 percent was upward flow from the bedrock. Discharge from the aquifer was to wells (68.9 percent) and to the Ohio River (31.1 percent). The simulated steady-state water budget for 1983 indicated that of the total recharge to the aquifer of 4.11 million feet per day, 42.6 percent was recharge from rainfall, 18.2 percent was flow across the eastern valley wall, 17.8 percent was flow from the river to pumped wells, 15.6 percent was upward flow from the bedrock, and 5.8 percent was flow from septic systems. The transient simulation resulted in an acceptable match between measured and simulated hydrographs. This gave additional confidence to the model calibration, choice of boundary conditions, and published values of specific yield. Both steady-state and transient-state models demonstrated that the main source of water needed to meet increased pumping requirements was induced flow from the Ohio River.