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A stochastic approach to steady‐state time‐related capture zone determination that is based on the conditional simulation of hydraulic conductivity is presented. Conditional simulation of hydraulic conductivity preserves the spatial correlation structure of the real hydraulic conductivity field as well as the measured, or known, values of hydraulic conductivity at sampling locations, thereby optimizing the use of available data and providing the most representative results possible. The stochastic analysis methodology utilizing conditional simulation is applied to a hypothetical ground‐water system with a water supply well to estimate uncertainty in the 1‐year and 10‐year capture zones of the well. The results demonstrate the influence of known hydraulic conductivity values on the estimates of uncertainty, as well as the behavior of the “zone of uncertainty” of the capture zone as a function of travel time and orientation of regional flow. The results have significant implications regarding strategies for sampling aquifer properties (e.g., hydraulic conductivity) for capture zone delineation and for interpretation of the effects of hydraulic conductivity uncertainty on capture zones.