The U.S. Geological Survey, in cooperation with the Kentucky Natural Resources and Environmental Protection Cabinet, constructed a two-dimensional, steady-state ground-water-flow model to estimate hydraulic properties, contributing areas to discharge boundaries, and the average linear velocity at selected locations in an aquifer system near Calvert City, Ky. Nonlinear regression was used to estimate values of model parameters and the reliability of the parameter estimates. The regression minimizes the weighted difference between observed and calculated hydraulic heads and rates of flow. The calibrated model generally was better than alternative models considered, and although adding transmissive faults in the bedrock produced a slightly better model, fault transmissivity was not estimated reliably. The average transmissivity of the aquifer was 20,000 feet squared per day. Recharge to two outcrop areas, the McNairy Formation of Cretaceous age and the alluvium of Quaternary age, were 0.00269 feet per day (11.8 inches per year) and 0.000484 feet per day (2.1 inches per year), respectively. Contributing areas to wells at the Calvert City Water Company in 1992 did not include the Calvert City Industrial Complex. Since completing the fieldwork for this study in 1992, the Calvert City Water Company discontinued use of their wells and began withdrawing water from new wells that were located 4.5 miles east-southeast of the previous location; the contributing area moved farther from the industrial complex. The extent of the alluvium contributing water to wells was limited by the overlying lacustrine deposits. The average linear ground-water velocity at the industrial complex ranged from 0.90 feet per day to 4.47 feet per day with a mean of 1.98 feet per day.