The contents and description in this book include the use and application of Mathematical and Statistical Modeling. The basic principles of flow (Darcy's Law and Mass Balance Equation) are used in describing basic flow of groundwater. It has been also shown that, how mathematical methods (FEM) integrated with newly advanced computer software tools (GMSH and FEniCS) are used for simulation of groundwater flow study. The mathematical methods (FEM) are used in analyzing real problems (Characteristics’ of hydraulic head in groundwater flow) with the help of computer aided programs. Simulation tool is finally developed and tested in different conditions for a specific water site system.