The objective of this study is to predict radionuclide solute transport process in the saturated zone below the Yucca Mountain project area. Based on a stochastic perturbation approach, a numerical method of moments has been developed and used to predict the mean, variance and upper bound of the radionuclide mass flux through a control plane 5-km downstream of the footprint of the repository. This study enhances the analysis of the effect of medium’s heterogeneity on solute transport prediction, especially on prediction uncertainty