Monte Carlo simulation is traditionally used for global sensitivity analysis using correlation matrix method with uncertain parameters. Uncertainty may be either due to variability or randomness or due to imprecision or fuzziness. Variability is addressed by probability density function and fuzziness is addressed by membership (triangular, or trapezoidal) function. Often it has been envisaged that the global sensitivity analysis in presence of mixture of both type of variables (random and fuzzy) is challenging. In fact, the task of sensitivity analysis with the model parameters which are fuzzy or imprecise in nature due to insufficient knowledge is challenging. Uncertainty modeling of a physical system at the design time is very important for decision making policies. But prior to uncertainty, actual influential parameters are required to determine. Model having countless unsure boundaries is required to go through the affectability examination to screen the most significant boundaries. The objective of this paper is to explore the application of Dempster Shafer evidence theory for sensitivity analysis and modeling uncertainty of a contaminant transport system (e.g. solute transport system).