Abstract: In this paper, the refining of naphthalene by parametric pumping fractional crystallization technique is studied. A mathematical model for batch multistage fractional crystallization is established based on principles of crytsallization and sweating. The Gauss - Newton method is used to give a numerical solution cnystalliztion of the model. The calculated results are consistent with the medial experimental values. This mathematical model is correct and can be the basis for scaling up parametric pumping fractional crystallization.