Failure to rigorously accommodate physical parameter uncertainty in groundwater transport models casts serious doubts on our ability to accurately delineate the contaminant plume at a given site. This failure could also considerably reduce the possibility of success of the remediation scheme intended to clean up a plume within the specified time. In this research, the probability that a contaminant leaking from a waste source will exceed some predetermined target level at a down-gradient well is estimated, along with the sensitivity of this probably to the basic uncertainty in input parameters. The relevant parameters are assumed random with prescribed probability distributions. We present a probabilistic modeling tool based on first- and second-order reliability methods (FORM and SORM) to account for parameter uncertainty in groundwater contaminant transport and remediation. The methodology is applied to analytical groundwater models to provide a simple screening tool for the assessment of contamination and remediation. In addition, numerical-based reliability models are developed to account for aquifer spatial heterogeneity and correlation structure in more complex systems.