A major tool used in the design of wellhead protection areas is the delineation of a capture zone for a pumping well by use of a simple, steady-state analytic solution. This simple approach has been useful for many small municipalities because of the high costs associated with obtaining the hydrogeologic information needed for detailed numerical modeling. This analytic solution, however, is deterministic, and uncertainty in the mean value estimates of the hydraulic parameters used in this model can be a major source of error in predicting capture zones. To address this problem, a statistical theory was developed for including the uncertainty in the transmissivity and the magnitude and direction of the hydraulic head gradient in the analytic solution for both the ultimate and time-dependent capture zone for an arbitrary reliability level. To demonstrate the method and investigate the effect of varying magnitudes of uncertainty on time-dependent capture zones, the method is applied to three synthetic data sets based on data from the Borden Aquifer in Ontario, Canada. In general, the results show that uncertainty in the length of the time-dependent capture zone at a given reliability level is dependent on the uncertainty in the magnitude of the mean regional flow, which is equal to the transmissivity multiplied by the hydraulic head gradient; uncertainty in the maximum width of the capture zone is dependent primarily on the uncertainty in the mean direction of the regional flow.