Inverse modeling has become a standard technique for estimating hydrogeologic parameters. These parameters are usually inferred by minimizing the sum of the squared differences between the observed system state and the one calculated by a mathematical model. The robustness of the least squares criterion, however, has to be questioned because of the tendency of outliers in the measurements to strongly influence the outcome of the inversion. We have examined alternative approaches to the standard least squares formulation. The robustness of these estimators has been tested by means of Monte Carlo simulations of a synthetic experiment, in which both non-Gaussian random errors and systematic modeling errors have been introduced. The approach was then applied to data from an actual gas-pressure-pulse-decay experiment. The study demonstrates that robust estimators have the potential to reduce estimation bias in the presence of noisy data and minor systematic errors, which may be a significant advantage over the standard least squares method. ¿ 1998 American Geophysical Union