The water-oil displacement process (from a rectangular reservoir) has been considered, that is described by a nonlinear system of partial differential equations with respect to the reservoir pressure (RP) and displacing phase saturation (DPS). Within the framework of the proposed model, the task of identifying the regime at the output boundary of the reservoir according to the specified conditions at the input boundary was set. The difference approximation method was used to construct a difference analogue of the problem, implicit with respect to RP and explicit with respect to DPS. As a result, an explicit formula was obtained for determining the approximate RP value at the outlet boundary of the reservoir at a given time layer. Taking into account the calculated RP distribution in the reservoir, the DPS distribution in the time layer was determined using an explicit formula. Based on the proposed computational algorithm, numerical experiments were carried out for the model oil reservoir.