The paper simulates the modes of a gas flow in a pipe closed at one end and open to the atmosphere at the other end; for this purpose, a numerical solution of the system of Navier – Stokes equations in a two-dimensional axisymmetric formulation has been used. The excitation of oscillations of gas-dynamic functions is caused by the temperature gradient in the pipe section resulting from the contact of the gas with differently heated toroidal elements inside the pipe, their temperature being maintained constant. When the specified gradient reaches the threshold value, a stable thermoacoustic oscillation of the gas column is observed in the pipe. The time dependences of the pressure and the axial component of the gas velocity, as well as the heat flows in the heat exchange unit of the resonator, were calculated. The obtained results were in good agreement with the experimental data.