The present work addresses the impact of the infiltration rate and the heterogeneity of soil on the hydrodynamic conditions in unsaturated underground flow regimes. A two dimensional finite element model was adopted to simulate the groundwater flow in porous media, which represented the flow of contaminated water through Darcian flow regimes. The porous regions were assumed unsaturated and anisotropic with a constant porosity. The study aimed to demonstrate the influence of rainfall on the mobility of contaminated water in underground soil layers in terms of the infiltration rate. The developed model provides a tool to predict the concentration of contaminants in highly polluted lands. In Kuwait, the Ahmadi area consists of three petroleum refineries (MAB, MAA, and SHU), which have been considered a potential source of underground water pollutants.