Self-oscillations of pressure arising in the elements of power equipment with an internal heat supply can, in some cases, impair the operation of this equipment. At high amplitudes of self-oscillations, conditions for its damage can be created. Thermoacoustic self-oscillations are a consequence of flow instability. A well-known example of processes accompanied by the generation of thermoacoustic self-oscillations is vibration combustion, which is observed in rocket engines, in air heaters for blast furnaces, etc. In order to determine the characteristics of pressure self-oscillations, numerical studies of natural convection in a vertical channel with internal local heat release are carried out. Heat release from internal sources occurs in a limited section of the channel, which is closer to the inlet cross section of the channel. At the outlet cross section of the channel, there is a system of coaxial cylindrical bodies that constitute additional local hydraulic resistance to air flow. The characteristics of the air flow in the channel, which are accompanied by self-oscillations of velocity and pressure, are determined from the numerical solution of the system of equations of dynamics and heat transfer for a compressible medium, taking into account the dependence of the thermophysical properties of air on temperature. Based on the results of this solution, the velocity, pressure and temperature fields in the flow are determined. It is shown that changes in flow velocity and pressure with time have the character of oscillations with variable amplitude. Velocity oscillations at the channel outlet are in antiphase with velocity oscillations at the channel inlet. The amplitudes and frequencies of these oscillations are found. The measures were determined to reduce the amplitude of pressure fluctuations in the flow. Among them - the dispersal of sources of internal heat release and a decrease in local hydraulic resistance. These measures can be applied to reduce the negative impact of self-oscillations on power equipment.