We present a method for inverse modeling in hydrology that incorporates a physical understanding of the geological processes that form a hydrologic system. The method is based on constructing a stochastic model that is approximately representative of these geologic processes. This model provides a prior probability distribution for possible solutions to the inverse problem. The uncertainty in the inverse solution is characterized by a conditional (posterior) probability distribution. A new stochastic simulation method, called conditional coding, approximately samples from this posterior distribution and allows study of solution uncertainty through Monte Carlo techniques. We examine a fracture-dominated flow system, but the method can potentially be applied to any system where formation processes are modeled with a stochastic simulation algorithm. ¿ 1998 American Geophysical Union