A new numerical method for the liquid-liquid extraction design has been developed and applied to quaternary systems. The method directly calculates the optimum number of equilibrium stages for a specified composition of the solutes in the product stream as well as the solvent flow rate; which satisfies the overall balance and the stage to stage calculations. The method is based on the geometrical concepts of the Ponchon and Savarit method for binary systems. A correlation of the solubility surface and the tie-line data is required in order to implement the calculation procedure. Different proposed methods with this objective are described in detail and applied to type 1 quaternary systems. Both experimental data and UNIQUAC-generated data have been used to illustrate the application which has been compared with the commercial design program ChemCad III, using the same thermodynamic model and the same binary parameters. The method has the advantage that it allows the direct design (determination of the number of stages for a given desired separation) and avoids the iterative calculations to solve the material balances and equilibrium conditions.