Well control in the process of their construction is one of the important factors in ensuring the safety of the technological process. Blowout preventer equipment, which includes annular preventers, is used to control the wells. This applies to oil and gas wells, and wells that provide degassing of coal seams to reduce their gas-dynamic activity. Technological processes of safe work require the expansion of the functionality of the sealing unit of the annular preventer while ensuring its high performance. One of the determining factors to ensure the required durability of seals in different modes of operation is the study of their stress-strain state. In this paper, the possibility of using simulation three-dimensional modeling in the study of the influence of the geometry of the reinforcing metal inserts of the seal on its stress-strain state as a whole is considered. To this end, a method for determining and determining the material constants for the implementation of the Mooney-Rivlin model, which describes the behavior of low-compressibility rubber in software products based on the finite element method. It is established that two material constants can be used for simulation modeling of an annular preventer seal with deformations not exceeding 150%. More constants must be determined to model a sealant with larger deformations (up to 600%). The reliability of the obtained results of the model studies is characterized by a total error of experimental and theoretical studies of up to 5%. Thus, the prerequisites are created and the possibility of using simulation modeling in the study and design of elements of universal preventers with high performance is confirmed.