The article describes physical and mathematical models of reservoir oxidation in oil deposits, the development of which is impossible with known technologies. In-formation oxidation is realized in the form of oil oxidation. A laboratory experiment on the core for the formation of combustion is presented, and the problems arising during the initiation of combustion in the rocks of the Bazhenov formation are described. It was revealed that the temperature gradient at the front and the rate of movement of the oxidation front are influenced by the volume of injected oxygen and the amount of kerogen per unit volume of the formation. The well-known Thomas model has been adapted for the analytical solution of the radial problem of in-situ combustion to the conditions of the implementation of oxidation processes in bituminous formations. The results of analytical calculations of the dynamics of changes in the formation temperature profile depending on the content of coking material and the flow rate of the injected air are presented. It was found that the temperature gradient at the front reaches 1,573 K/m, and that the rate of oxidation movement is influenced by the volume of oxygen and the density of kerogen reserves in the formation. Recommendations are made for further study of the advance of the front of intra-layer combustion in order to clarify the dependencies of the influence of other parameters (permeability, water saturation, etc.) on the speed of the front advance.