A digital model of the Mississippi River Valley alluvial aquifer in eastern Arkansas was used to simulate ground-water flow for the period from 1918 to 2049. The model results were used to evaluate effects on water levels caused by demand for ground water from the alluvial aquifer, which has increased steadily for the last 40 years. The model results showed that water currently (1998) is being withdrawn from the aquifer at rates greater than what can be sustained for the long term. The saturated thickness of the alluvial aquifer has been reduced in some areas resulting in dry wells, degraded water quality, decreased water availability, increased pumping costs, and lower well yields. The model simulated the aquifer from a line just north of the Arkansas-Missouri border to south of the Arkansas River and on the east from the Mississippi River westward to the less permeable geologic units of Paleozoic age. The model consists of 2 layers, a grid of 184 rows by 156 columns, and comprises 14,118 active cells each measuring 1 mile on a side. It simulates time periods from 1918 to 1998 along with further time periods to 2049 testing different pumping scenarios. Model flux boundary conditions were specified for rivers, general head boundaries along parts of the western side of the model and parts of Crowleys Ridge, and a specified head boundary across the aquifer further north in Missouri. Model calibration was conducted for observed water levels for the years 1972, 1982, 1992, and 1998. The average absolute residual was 4.69 feet and the root-mean square error was 6.04 feet for the hydraulic head observations for 1998. Hydraulic-conductivity values obtained during the calibration process were 230 feet per day for the upper layer and ranged from 230 to 730 feet per day for the lower layer with the maximum mean for the combined aquifer of 480 feet per day. Specific yield values were 0.30 throughout the model and specific storage values were 0.000001 inverse-feet throughout the model. Areally specified recharge rates ranged from 0 to about 30 inches and total recharge increased from 1972 to 1998 by a factor of about four. Water levels caused by projected ground-water withdrawals were simulated using the calibrated model. Simulations represented a period of 50 years into the future in three scenarios with either unchanged pumpage, pumpage increased by historic trends, or pumpage increased by historic trends except in two areas of the Grand Prairie. If pumping remains at 1997 rates, this produces extreme water-level declines (areas where model cells have gone dry or where the water level in the aquifer is equal to or less than the original saturated thickness, assuming confined conditions in the aquifer everywhere in the formation in predevelopment times) in the aquifer in two areas of the aquifer (one in the Grand Prairie area between the Arkansas and White Rivers and the other west of Crowleys Ridge along the Cache River) with about 400 square miles going dry. Increasing the pumping rates to that which would be projected using historic data led to increased extreme water-level declines in both areas with about 1,300 square miles going dry. Declines in both scenarios generally occurred most rapidly between 2009 and 2019. Reducing the pumping rates to 90 percent of that used for projected historic rates in areas between the Arkansas and White Rivers relating to two diversion projects of the U.S. Army Corps of Engineers and other agencies did little to decrease the extreme water-level declines. However, these pumpage reductions are small (amounting to about 16 percent of the reductions that could result from implementation of these diversion projects).