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The article is devoted to the development of a sprinkling process model that is in relation to the probabilistic similarity to the simulated process, the numerical implementation of which allows to calculate the matrix of irrigation doses in the sprinkling area, or at the test site. The study was performed using system analysis and probabilistic modeling. The uniform distribution of fluid over the area until 2004 was estimated by the RD 10.11.1-9-89 by the effective irrigation coefficient, insufficient irrigation coefficient, and excessive irrigation coefficient. After the introduction of the interstate standard ISO 7749-2-2004 it is estimated by the Christiansen coefficient. New mathematical models and software were designed for probabilistic modeling of the sprinkling process. In constructing the model, the event combining theorem and the Lyapunov theorem were u sed. As the example, analysis of the operation of twelve sprinklers was carried out. The presented computational experiment was performed to optimize the positioning of the apparatuses according to the criteria of irrigation uniformity and the coefficient of ac-counting completeness of water, which falls on the test site. The obtained results can be used in the process of optimizing the placement of vehicles on «Volzhanka» and «Dnepr» machines. Probabilistic mathematical models of the sprinkling process make it possible to optimize the positioning of apparatuses according to the criteria of uniform irrigation. The programs for modeling water distribution by devices from four positions are applicable only when the distance between the positions is greater than the radius of the sprinkling zone. Irrigation uniformity indicators do not meet agrotechnical requirements. Optimization of the positioning of the apparatus in twelve positions provides excellent indicators for irrigation uniformity.The optimization programs and techniques that were used in the study are applicable to optimize the distribution of other liquids in agricultural technologies, for example, for the distribution of pesticides.

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