The advantages of mathematical simulations of the process of cured hide desalination are presented. Full three-dimensional model is presented and then its one-dimensional and a two-dimensional special cases are considered and compared. In the case of one-dimensional approximation, the solution can be obtained in an analytic form, while for the two-dimensional case only numerical solution is available. A possible occurrence of a concentration shock is modelled, and a method of its prevention is proposed to reduce losses in the hide substance. The predictions of the mathematical model are then compared with experimental data and found to be in good agreement.