This paper describes a new technique for conditional simulation of aquifer properties in unobserved regions. The technique utilizes a recently introduced model for heterogeneity based on the L¿vy-stable family of probability distributions to achieve a higher degree of realism than is possible with Gaussian-based techniques. Specifically, permeability and porosity variations are modeled using fractional L¿vy motion. A new algorithm for producing fractional L¿vy motion conditioned to match known data is introduced. Two-dimensional simulations using actual permeability measurements as input demonstrate that this algorithm produces random fields with the specified properties. Simulations using a subset of a detailed permeability map of an outcrop as input illustrate how the new method can be used to estimate important flow and transport properties and to quantify uncertainties in these estimates. ¿ American Geophysical Union 1996