A digital model using finite-difference techniques was constructed to simulate ground-water flow in an alluvial aquifer on the Nisqually Indian Reservation. The maximum long-term rate of pumping from individual wells, based on available data, is about 0.75 cubic feet per second (340 gallons per minute). Data on the extent, hydraulic conductivity, saturated thickness of the alluvial aquifer, and quality of the ground water was obtained primarily from the more than 22 test holes drilled for this project. The test holes ranged in depth from about 10 to 100 feet. The saturated thickness of the alluvium was found to range generally from about 10 to 60 feet in the area investigated. The water table is usually less than 10 feet below land surface. The hydraulic conductivity of the aquifer was determined to range from 8.5 to 170 feet per day. The leakage coefficient of the river bed material was determined to be about 0.06 foot per day. Rainfall recharge to the aquifer is about 10 inches per year. A U.S. Geological Survey two-dimensional digital computer model was calibrated to simulate ground-water flow in the alluvial aquifer (area investigated is about 1.1 square miles). The calibrated model simulated measured water levels in the alluvial aquifer to within about 1 foot at 13 of 17 test well locations throughout the model area and within 2 feet at 16 of 17 test well locations. When pumping from the alluvial aquifer was simulated with the computer model it was found that 90 to 100 percent of the water pumped from wells was derived from induced recharge from the Nisqually River into the aquifer and (or) reduced discharge from the aquifer to the Nisqually River. Wells drilled for a large demand use such as a fish hatchery supply will achieve the highest yield if they are placed close to the Nisqually River and in the areas of greatest saturated thickness and highest permeability of the aquifer. (USGS)