Abstract. 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. based on geologic theory. We solve the inverse modeling problem by using this stochastic model to define a broad suite of possible spatial structures, and we then select samples from this suite that are consistent with (i.e., conditioned upon) the available hydraulic response data. The resulting solution is a model that is consistent with flow data and the geologic theory represented in the stochastic model. Our inverse modeling method is Bayesian, so we give a brief description of Bayesian theory and introduce some notation. In the Bayesian approach one first assumes that the unknown hydraulic geometry is randomly chosen from a given probability distribution of possible hydraulic geometries. This distribution is called the prior distribution or just the prior. Probabilities given by the prior can be represented with the notation P(X = X), where X represents the random hydraulic geometry and X is a particular geometry that X could equal. Before data are collected, the prior contains the only information about possible values for X, but after the data are taken some Xs will be more compatible with the data and so become more probable while other Xs are less compatible and less probable. Our Bayesian approach has two main components. First we define X using a physically based stochastic model that represents the geologic processes that form a hydraulic geometry; 3335