A three-dimensional finite-difference model of groundwater flow was used to estimate the hydraulic conductivity of riverbed and aquifer material in a 1-square-mile valley-fill aquifer system near a large river in which induced infiltration due to pumping cannot be measured directly. The aquifer consists of a 30- to 70-foot thickness of sand and gravel containing discontinuous layers of compact and silty sand and gravel. Horizontal hydraulic conductivity of the aquifer material, estimated through trial-and-error calibration of simulated water levels to drawdowns measured during an aquifer test, ranged from 500 to 10,000 feet per day; anisotropy (ratio of horizontal to vertical hydraulic conductivity) ranged from 125:1 to 250:1. The vertical hydraulic conductivity of the riverbed was estimated to be 0.1 to 0.5 foot per day, whereas permeameter tests on samples of silty sand and gravel layers from the riverbed yielded vertical hydraulic conductivity of 10 -3 foot per day. A sensitivity analysis indicated that a narrow range of anisotropy values gave the smallest residual error in simulated drawdowns. Residual error increased sharply when the maximum hydraulic conductivity value for the aquifer was lowered to less than 5,000 feet per day. Residual error also was large for large values of vertical hydraulic conductivity of the riverbed, but decreased to a constant amount for values less than 0.1 foot per day. Residual error was relatively insensitive to changes in the storage coefficient and specific yield. A nonlinear regression method that approximated the sensitivity matrix with a perturbation technique was applied to refine the estimates of these parameters and compute standard error of the estimates. The nonlinear regression indicated that the model was sensitive to hydraulic conductivity of the aquifer and anisotropy of the upper part of the aquifer but not to anisotropy of the lower part, and that vertical hydraulic conductivity of the riverbed was less than 0.5 foot per day. The regression method yielded aquifer hydraulic-conductivity values of 210 to 13,000 feet per day and an anisotropy ratio of 350:1 for the upper part of the aquifer; the standard error of these estimates was relatively small. In contrast, the standard errors of estimates of anisotropy in the lower part of the aquifer and the vertical hydraulic conductivity of the riverbed were extremely large.