The unsteady drawdown distribution around a non-penetrating well discharging from an extensively thick confined aquifer has been obtained. The solution is expressed in terms of dimensionless time factor and well function similar to the Theis method. However, the basic parameters are the hydraulic conductivity and specific storage coefficient. It is found that the type curves for non-penetrating wells is identical to the Theis type curve. Classical matching procedure leads to the determination of the specific storage and hydraulic conductivity coefficients.