According to the 'Law of the River', wells that draw water from the Colorado River by underground pumping need an entitlement for the diversion of water from the Colorado River. Consumptive use can occur through direct diversions of surface water, as well as through withdrawal of water from the river by underground pumping. To develop methods for evaluating the need for entitlements for Colorado River water, an assessment of possible depletion of water in the Colorado River by pumping wells is needed. Possible methods include simple analytical models and complex numerical ground-water flow models. For this study, an intermediate approach was taken that uses numerical superposition models with complex horizontal geometry, simple vertical geometry, and constant aquifer properties. The six areas modeled include larger extents of the previously defined river aquifer from the Lake Mead area to the Yuma area. For the modeled areas, a low estimate of transmissivity and an average estimate of transmissivity were derived from statistical analyses of transmissivity data. Aquifer storage coefficient, or specific yield, was selected on the basis of results of a previous study in the Yuma area. The USGS program MODFLOW-2000 (Harbaugh and others, 2000) was used with uniform 0.25-mile grid spacing along rows and columns. Calculations of depletion of river water by wells were made for a time of 100 years since the onset of pumping. A computer program was set up to run the models repeatedly, each time with a well in a different location. Maps were constructed for at least two transmissivity values for each of the modeled areas. The modeling results, based on the selected transmissivities, indicate that low values of depletion in 100 years occur mainly in parts of side valleys that are more than a few tens of miles from the Colorado River.