Non-equilibrium groundwater movement equations are written explicitly for the continuity and flow laws in the case of a non-penetrating large diameter well discharging from extensively thick confined porous medium aquifers. The equations representing these laws are combined together with the Boltzmann transformation which leads to the specific discharge equation within the aquifer. Type curve expressions are obtained with convenient definitions of the well function and dimensionless time factor for a non-penetrating well. The forms of these curves on double logarithmic paper appear identical to the fully penetrating large diameter well type curves but with differences in the variables as well as the aquifer parameters. In the non-penetrating well case the significant aquifer parameters are the hydraulic conductivity and specific storage coefficient which are intact of the aquifer saturated thickness. The methodology developed herein is applied to the time-drawdown data from a non-penetrating well in Saudi Arabia. Aquifer parameter determinations can be obtained through a similar procedure to the Theis type curve usage.