The paper proposes an approach to the numerical solving the problem of determining the parameters of a two-dimensional mathematical model of oil filtration. The parameters are determined on the class of piecewise constant functions. It is important that in this case the problem is not only to identify parameters values, but also to identify the parameters constancy boundaries. The approach is based on reducing the initial identification problem to a finite-dimensional optimization problem of a network structure. To solve this finite-dimensional optimization problem we obtain formulas for the gradient of the functional in the space of coefficient values that determine the process parameters and the domain of constancy of the coefficients. These formulas allow to use effective first-order optimization methods, in particular, the gradient method. Some of the results of the carried out computer experiments are given. The obtained results show the efficiency of the proposed approach to the numerical solving the identification problem.