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The relevance of the study is caused by the fact that differential tacks are one of the most difficult accidents in the entire technological chain of construction of oil and gas wells. A high quality and correctly selected drilling mud with optimal rheology for specific drilling conditions is one of the determining factors in preventing differential tacks. Goal: development of a neural network rheological model of drilling mud based on its component composition and the results of periodic measurements of the output parameters of the flushing fluid. With the help of a neural network, it is possible to accurately and quickly predict the values of the rheological properties of the solution, which have a significant impact on the occurrence and prevention of differential seizures. Object: neural network rheological models of drilling mud, drilling muds, which composition affects the rheological properties and the possibility of preventing differential sticking of the drill string during well construction. Methods: neural network model of drilling mud differing in the number and composition of input parameters is proposed. Results. The paper describes the learning process of three neural networks based on operational data obtained on instruments for measuring drilling mud parameters. The authors proposed six types of drilling muds that are optimal for specific geological conditions. Introduction of nanodispersed copper and potassium aluminate into the composition of a drilling mud with a high lubricity helps to reduce the friction coefficient, increase the inhibitory ability of the solution, reduce water loss and, as a result, decrease sharply the differential tack during the construction of wells on hydrocarbon raw materials.