The potential effects of water-management plans on stream-aquifer systems in several countries have been simulated using electric-analog or digital-computer models. Many of the electric-analog models require large amounts of hardware preparation for each problem to be solved and some become so bulky that they present serious space and access problems. Digital-computer models require no special hardware preparation but often they require so many repetitive solutions of equations that they result in calculations that are unduly unwieldy and expensive, even on the latest generation of computers. Further, the more detailed digital models require a vast amount of core storage, leaving insufficient storage for evaluation of the many possible schemes of water-management. A concept introduced in 1968 by the senior author of this report offers a solution to these problems. The concept is that the effects on streamflow of ground-water withdrawal or recharge (stress) at any point in such a system can be approximated using two classical equations and a value of time that reflects the integrated effect of the following: irregular impermeable boundaries; stream meanders; aquifer properties and their areal variations; distance of the point from the stream; and imperfect hydraulic connection between the stream and the aquifer. The value of time is called the stream depletion factor (sdf). Results of a relatively few tests on detailed models can be summarized on maps showing lines through points of equal sdf. Sensitivity analyses of models of two large stream-aquifer systems in the State of Colorado show that the sdf technique described in this report provides results within tolerable ranges of error. The sdf technique is extremely versatile, allowing water managers to choose the degree of detail that best suits their needs and available computational hardware. Simple arithmetic, using, for example, only a slide rule and charts or tables of dimensionless values, will be sufficient for many calculations. If a large digital computer is available, detailed description of the system and its stresses will require only a fraction of the core storage, leaving the greater part of the storage available for sophisticated analyses, such as optimization. Once these analyses have been made, the model then is ready to perform its principal task--prediction of streamflow and changes in ground-water storage. In the two systems described in this report, direct diversion from the streams is the principal source of irrigation water, but it is supplemented by numerous wells. The streamflow depends largely on snowmelt. Estimates of both the amount and timing of runoff from snowmelt during the irrigation season are available on a monthly basis during the spring and early summer. These estimates become increasingly accurate as the season progresses, hence frequent changes of stress on the predictive model are necessary. The sdf technique is especially well suited to this purpose, because it is very easy to make such changes, resulting in more up-todate estimates of the availability of streamflow and ground-water storage. These estimates can be made for any time and any location in the system.