A new method based on the depression cone volume concept is presented for the identification of hydraulic parameters of leaky aquifers with additional elastic storage release from the unpumped aquifer, The solution deals with the flow system by first considering the continuity equation based on the unpumped and pumped aquifers and constant. pump discharges, The elastic storage coefficients are taken into account individually by relating them to the depression cone volumes. In addition, the unpumped aquifer flow is assumed to be transmitted to the pumped aquifer through the aquitard according to a pseudo steady-state Row law, The resulting first-order ordinary differential equation in terms of the depression cone volume is solved, leading to time-variant unpumped and pumped aquifer discharge expressions, The pumped aquifer is then considered as a confined aquifer with variable discharge to the well. The results are presented as type curves, which reduce to the Theis and Hantush solutions if the storage coefficient of the unpumped aquifer is neglected. The type-straight-line method is developed for hydraulic parameter estimations based on late time-drawdown data. The method is general and includes the De Glee steady-state and Jacob straight-line solutions as special cases. A dimensionless time-drawdown plot is proposed to determine whether the aquifer is leaky or nor. Necessary steps in the application of the methodology are presented with actual field data.