Management of wells in the process of their construction is one of the important factors in ensuring the safety of the technological process. Blowout equipment, which includes annular preventers, is used to control the wells. This applies to the construction of oil and gas wells, or wells that provide degassing of coal seams to reduce their gas-dynamic activity. For the purpose of safe and long-term operation of annular preventers on the basis of the theory of thick-walled combined reinforced shells and the carried-out analytical research, the mathematical model for research of a stress-strain condition of a seal of an annular preventer has been offered. Taking into consideration the real design, the seal of the annular preventer is modeled by a rubber shell, reinforced in the circular direction by rubber frames, and in the longitudinal direction by metal stringers. The mathematical model provides for determining the stiffness, internal force factors and stresses in the longitudinal and transverse sections of the combined rubber-metal seal, considering the peculiarities of its operation. At the same time, the model includes the conditions of interaction of the rubber base of the seal with a pipe, as well as the action of sealing pressure under operating conditions. The use of the proposed mathematical model reduces the costs of experimental research and will contribute to ensuring the reliability of simulation modeling results. The advantage of the method is the determination of calculated loads at different points of the combined seal under the existing state of dangerous zones and the influence of operating conditions. In the meantime, prerequisites have been created for expanding the possibilities of simulation modeling and designing structural elements of annular preventers with increased operational characteristics. The practical value of the obtained results is determined by the possibility of using them to ensure the performance of the rubber-metal seal both at the stage of its design and during the operation.