Numerical simulation is used for studying the propagation of slow laser-supported combustion waves (LCW) in atmospheric air. The gasdynamic structure is investigated of the flow field which accompanies the movement of laser-supported combustion wave. A special feature of the problem being solved is the inclusion of gravity; this results in the emergence of convective motions in the thermal wake of LCW. It is demonstrated that different modes of thermal gravitational convection are observed depending on the conditions of LCW movement. A two-dimensional radiation-gasdynamic model is given, which includes the continuity and Navier-Stokes equations, the energy equation, and the equations of laser and thermal radiation transport in a multi-group approximation. The real thermal and spectral optical properties of air in the temperature range from 300 to 20 000 K are taken into account.