A stochastic continuum model of a fractured medium conditioned on a specific set of field data is developed. Both the more conductive fractures and the less permeable matrix are generated within the framework of a single-continuum stochastic model based on nonparametric indicator geostatistics. In the stochastic model the fracture zones are distinguished from the matrix by imposing a long-range correlation structure for a small fraction (the highest approximately 11%) of the hydraulic conductivity in the preferred planes of fracture zones. Results of flow and transport simulation in three dimensions (3D) are used to illustrate the large spatial variability of point measurements, but for spatially integrated quantities the variability is reduced and results become less sensitive to correlation structure. Therefore it is suggested that spatially integrated quantities may be a more appropriate choice for predicting flow and transport in a strongly heterogeneous medium in that they are more commensurate with the level of our ignorance of the site. The issue of spatial variability giving rise to uncertainty in the site characterization of a heterogeneous medium and the prediction of transport results is also addressed. Simulations are carried out for 3D transport from point tracer sources at hundreds of locations in the medium. The breakthrough curve from each point source release is characterized by two parameters: the mean transport velocity and the dispersion coefficient. The results are presented as a statistical distribution of the transport parameters, thus quantifying the uncertainty in predicting flow and transport based on a limited amount of site characterization data. ¿ American Geophysical Union 1996