An important issue for the long-term performance of underground nuclear waste repositories is the rate of water seepage into the waste emplacement drifts. A prediction of the seepage rate is particularly complicated for the potential repository site at Yucca Mountain, NV, which is located in a thick sequence of unsaturated, fractured tuffs. Underground openings in unsaturated media might act as capillary barriers, diverting water around them. In the present work, we study the potential rates of seepage into drifts as a function of predicted percolation flux at Yucca Mountain, based on a stochastic model of the fractured rock mass in the drift vicinity. A variety of now scenarios are considered, assuming estimated present-day and predicted future climate conditions. We show that the heterogeneity in the flow domain is a key factor controlling seepage rates, since it causes channelized flow and local pending in the unsaturated flow field. The rates of seepage are related in a complex non-linear manner to the rock properties, the size and shape of the drift, the degree of heterogeneity, and the assumed percolation scenario. (C) 1999 Elsevier Science B.V. All rights reserved.