The methods presented in this work provide a potential tool for characterizing contaminant source zones in terms of mass flux. The problem was conceptualized by considering contaminant transport through a vertical "flux plane" located between a source zone and a downgradient region where contaminant concentrations were measured. The goal was to develop a robust method capable of providing a statement of the magnitude and uncertainty associated with estimated contaminant mass flux values. In order to estimate the magnitude and transverse spatial distribution of mass flux through a plane, the problem was considered in an optimization framework. Two numerical optimization techniques were applied, simulated annealing (SA) and minimum relative entropy (MRE). The capabilities of the flux plane model and the numerical solution techniques were evaluated using data from a numerically generated test problem and a nonreactive tracer experiment performed in a three-dimensional aquifer model. Results demonstrate that SA is more robust and converges more quickly than MRE. However, SA is not capable of providing an estimate of the uncertainty associated with the simulated flux values. In contrast, MRE is not as robust as SA, but once in the neighborhood of the optimal solution, it is quite effective as a tool for inferring mass flux probability density functions, expected flux values, and confidence limits. A hybrid (SA-MRE) solution technique was developed in order to take advantage of the robust solution capabilities of SA and the uncertainty estimation capabilities of MRE. The coupled technique provided probability density functions and confidence intervals that would not have been available from an independent SA algorithm and they were obtained more efficiently than if provided by an independent MRE algorithm.