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Procedures are presented for delineating capture zones of pumping wells. First, an algorithm is presented for determining the envelopes of the capture zones by the use of the locations of stagnation points. Second, it is discussed how the streamlines are determined that separate groundwater originating from different sources (the dividing streamlines). Third, a procedure is presented for constructing the boundary of the capture zone for any given time. The procedures are implemented in an analytic element code and are applied to groundwater flow systems that can be modeled with wells, line sinks, uniform flow, and areal infiltration.