A three-dimensional finite-difference model for part of the Mississippi River Valley alluvial aquifer in the Cache Critical Groundwater Area of eastern Arkansas was constructed to simulate potential future conditions of groundwater flow. The objectives of this study were to test different pilot point distributions to find reasonable estimates of aquifer properties for the alluvial aquifer, to simulate flux from rivers, and to demonstrate how changes in pumping rates for different scenarios affect areas of long-term water-level declines over time. The model was calibrated using the parameter estimation code. Additional calibration was achieved using pilot points with regularization and singular value decomposition. Pilot point parameter values were estimated at a number of discrete locations in the study area to obtain reasonable estimates of aquifer properties. Nine pumping scenarios for the years 2011 to 2020 were tested and compared to the simulated water-level heads from 2010. Hydraulic conductivity values from pilot point calibration ranged between 42 and 173 m/d. Specific yield values ranged between 0.19 and 0.337. Recharge rates ranged between 0.00009 and 0.0006 m/d. The model was calibrated using 2,322 hydraulic head measurements for the years 2000 to 2010 from 150 observation wells located in the study area. For all scenarios, the volume of water depleted ranged between 5.7 and 23.3 percent, except in Scenario 2 (minimum pumping rates), in which the volume increased by 2.5 percent.