In order to apply the numerical method to practical groundwater flow problem in the field, the hydraulic properties must be estimated. In this paper, new methods of analyzing drawdown tests were developed and illustrated with some examples to determine hydraulic properties of aquifer. Drawdown tests sometimes have to be performed near the boundary of the aquifer or in the much groundwater supplied aquifer. In such instances, the assumption that the aquifer is of infinite areal extent is no longer valid. Therefore the analytical solutions of unsteady flow due to drawdown test are derived in the conception of "Island Model" that the shape of groundwater level is fixed by the circular water supply which is equilibrium with the pumping rate. By using these solutions, new methods of analyzing drawdown tests which are performed in a confined aquifer and an unconfined aquifer were given respectively and the effect of influence region was evaluated. The example analysis to determine permeability and storage coefficient were shown. As the results,the propriety of the solutions is verified comparing the analytical results with the drawdown test data taken from a real aquifer project.