Self-propagating high-temperature synthesis (SHS) is a combustion process involving two or more solid reactants. The typical SHS configuration consists of a cylindrical preform of mixed powders, placed in an inert gas chamber, and ignited at one end. In past studies, interaction between the solid phase and the ambient gas phase has been limited to heat losses from the solid; the influence of natural convection on the solid phase has never been considered. In this study, computational fluid dynamics (CFD) is used, and it is shown that intense convection flow develops in the proximity of the combustion front. Gas flows adjacent to reacted solid material, heats up, and when it reaches the unreacted solid heat is transferred from the gas to the solid phase, which aids solid phase thermal conduction in preheating the material. The effect is stronger than expected, and it could stabilize the combustion of structured reactants like roll-ups of foils and wires. Combustion parallel and antiparallel to gravity is investigated for different burning velocities. At low propagation velocities, the natural convection cell forms a torus that is seated above the combustion front. At high propagation velocities, the convection flow cannot track the combustion front, and Tolimien-Schlichting waves form. Constant front propagation and planar oscillations of the combustion front lead to increasingly complex flows. Finally, the heat exchange between the gas and solid for constant front propagation is compared to analytical solutions.