Reliability algorithms provide attractive alternatives to Monte Carlo simulation and stochastic perturbation approaches for probabilistic analysis of contaminant transport in porous media. We describe results and issues for further study based on a first-order reliability analysis in conjunction with a two-dimensional finite element model of transport in porous media. Probabilistic sensitivity measures provide valuable information on the importance of the uncertain variables - particularly the spatially discretized permeability values. An example flow region is analyzed and longitudinal dispersivity, fluid density, solid grain density, and distribution coefficient have the greatest influence on the probabilistic outcome. These are all global uncertain variables, as opposed to the discretized permeability uncertain variables. The authors' previous work with analytical transport solutions indicated dispersivity had little influence on the probabilistic outcome; rather, those models were dominated by the uncertainty in flow velocity and the reaction terms.