Summary: The material discontinuity profile along the separation surface between the liquid and solid phases may represent a difficulty for the numerical solutions in studies of groundwater flow and contaminant transport in porous media and fractured systems. The present paper focuses on the dispersion of an hydrosoluble pollutant where the numerical procedures are required to describe the discontinuity of the concentration profile and at the same time preserve the continuity of the mass flux. The analysis shows that, whenever the use of shifted computational grid offers the possibility of a particularly elegant approach, the use of nonshifted computational grid should be preferred.