We present a stochastic approach to characterize the uncertainty in the delineation of well capture zones. Hereby, we account for both the uncertainty that stems from the natural variability of the transmissivity field and the uncertainty inherent in estimating the parameters of the stochastic model of the transmissivity field. We show how transmissivity measurements and hydraulic head observations are incorporated in a Bayesian framework to obtain posterior probabilities for individual realisations of the transmissivity field. In prediction, the realisations are weighted by their respective posterior probabilities, yielding the predictive capture zone distribution. We apply the method to a hypothetical flow system and compare the worth of transmissivity measurements and head observations by incorporating the different data types into the estimation procedure sequentially.