This work evaluated the performance of a combustion chamber operating with a self-recuperative burner at various atmospheric pressures by means of Computational Fluid Dynamics (CFD) simulation. The aim was to determine the effect of atmospheric pressure on the main variables of the combustion system through mathematical correlations and numerical simulations. Parameters such as heat transfer from flue gases to the load, fluid dynamic inside the combustion chamber volume, exhaust gas composition, and burner effectiveness were monitored to analyze the performance of the reheating furnace and the self-recuperative burner. Three atmospheric pressure conditions were examined: 1 atm, 0.85 atm, and 0.74 atm. The simulations used an axisymmetric 2D geometry of the system in steady state, where the heat exchanger of the self-recuperative burner was considered. The CFD results indicated that atmospheric pressure did not have a significant effect on the performance of the combustion and heating systems when the mass flows of fuel, combustion air and ejection air were corrected for the effects of atmospheric pressure. However, when these mass flows were not corrected, the average temperature of the process decreased, while the concentration of CO and CO2 in the exhaust gases increased and the heat transfer on the load by radiation decreased. Finally, the performance of the self-recuperative burner remained constant with atmospheric pressure if the mass flows were corrected, and increased when the mass flows were not corrected.