The 7,000-square-mile Mississippi River alluvial plain in northwestern Mississippi, locally known as the 'Delta,' is underlain by a prolific aquifer that yielded about 1,100 million gallons per day of water to irrigation wells in 1983. About 20 feet of clay underlying the Delta land surface commonly is underlain by about 80 to 180 feet of sand and gravel that forms the Mississippi River alluvial aquifer. This study of the alluvial aquifer was prompted by recent declines of water levels. The study was designed to better define the hydrology of the aquifer and to quantify availability of water from the aquifer. The Mississippi River is in good hydraulic connection with the alluvial aquifer. Generally, smaller streams are less likely to recharge the aquifer than larger streams. Direct vertical recharge to the alluvial aquifer from the 52 inches per year of precipitation is small, especially in the central part of the Delta. A two-dimensional finite-difference computer model of the alluvial aquifer was constructed, calibrated, and verified using water levels observed for five dates from April 1981 to September 1983. The values of some of the calibration-derived parameters are hydraulic conductivity, 400 feet per day; specific yield, 0.30; and infiltration of precipitation to the aquifer, 0.5 inch per year. The model showed that the aquifer had a net loss in storage of about 360 million gallons per day from April 1981 to April 1983. During this period, pumpage was about 1,100 million gallons per day (1,270,000 acre-feet per year), and the net inflows from the sources of recharge were as follows, in million gallons per day: Mississippi River, 390; recharge along the east edge of the Delta, 170; streams within the Delta, 57; areal recharge from infiltration, 180; and oxbow lakes, 24. The effects of several levels of pumpage by wells--0, 670, 1,100, 1,900, and 4,000 million gallons per day--were projected 20 years into the future. In 2003, the 1,100-milliongallon-per-day pumping rate, about average for the early 1980's, would take 46 percent of the water withdrawn from aquifer storage, water levels would be lowered more than 20 feet in a large area in the central part of the Delta, and groundwater levels would continue to decline in future years.