Purpose. Research of thermodynamic and geomechanical processes occurring in a gas hydrate body under the influence of an activating agent (sea water from surface layers) in the conditions of the Black Sea by mathematical modeling using finite element method.Methods. The modeling of thermodynamic and geomechanical processes is performed with the use of ANSYS v17.0 software and in accordance with the climatic, hydrogeological and physic-mechanical properties of the numerical model elements in the Black Sea gas hydrate deposit under consideration, which are similar to natural ones. The thermodynamic processes were studied in the section "Steady-State Thermal", and the geomechanical (stress-strain state) in "Static Structural".Findings. The spatial model is developed, which allows to simulate thermodynamic and geomechanical processes in a gas hydrate body under the influence of a thermal agent. As a result of modeling, it was determined that under these conditions the temperature in the gas hydrate body varies with the distance from the production well similarly in both directions according to the polynomial dependence. What is more, at a distance from the well of 18.7 m the temperature is stable and equals +22°С, and in the range of 18.7 -24.9 m -decreases by 3.1 times and reaches a value of +7°С. It was found out that deformations in a gas hydrate body under the influence of an activating agent, which is fed under pressure above the initial, are directed from the lateral boundaries to the center of the gas hydrate body in the direction of productive dissociation zones. This, in its turn, results in the displacement of the gas hydrate volume to the reaction proceeding center, improving the quality of the decomposition process and allows mining of 87 -91% gas hydrate volume, which is presented in the model. Originality. For the first time, for the conditions of the Black Sea gas hydrate deposits, an analytical assessment of the dissociation zone distribution from the production well under the influence of the thermal agent and the changes of the stress-strain state of the gas hydrated body during its decomposition, has been carried out. This allows to improve the technology of the gas hydrate deposits development in the conditions under consideration.Practical implications. The technological scheme for the development of a gas hydrate body based on the combined approach to the effects of activators (temperature and pressure) is proposed, which eliminates the need to warm the boundary sections of the deposit and increases the amount of the supplied activating agent and its temperatures, which in its turn leads to a decrease in the resource-and energy consumption.