In this paper, a mathematical modeling of differential quadrature method is developed to characterize the drawdown of water due to pumping in a well. Polynomial differential quadrature method (PDQM) is applied to the solution of governing equations with boundary and initial conditions for confined and unconfined aquifers in unsteady flow and radial flow. Differential quadrature method is utilized for governing equation of flow with boundary condition tending to infinity. Accuracy, smoothness and efficiency of the obtained results are verified and compared with analytical solutions. Further, parametric studies are introduced to produce realistic results of head distribution. Four cases of different aquifer-aquitard systems are described to verify the numerical modeling of pumping test to predict the head.