In this paper, a new model simplification method, thermodynamic equilibrium analysis solver, and solvent extraction process simulator are developed for the modeling and simulation of the solvent extraction process with saponified PC88A for purifying rare earth metals. Firstly, the number of nonlinear equilibrium equations to be simultaneously solved is decreased by the proposed model simplification method such that the initial guess problems and poor convergence or divergence problems associated with solving the nonlinear equations can be overcome. Secondly, a new thermodynamic equilibrium analysis solver combined with the proposed model simplification method is proposed to estimate the equilibrium concentrations of the rigorous first principle equilibrium model without any numerical problems. Thirdly, a solvent extraction process simulator combined with the proposed thermodynamic equilibrium analysis solver is developed to estimate all the concentrations of all stages of the solvent extraction process. Simulation study has confirmed that the proposed method can simulate the solvent extraction process without numerical problems such as the initial guess problems and poor convergence or divergence problems. A trial version of the rare earth solvent extraction process simulation software is freely available on the web at http://pse.knu.ac.kr. The proposed modeling and simulation method can contribute immensely to the efficient design of the solvent extraction process with saponified PC88A.