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 corresponding to different meters above sea level (masl) altitudes: 1 atm (0 masl), 0.85 atm (1550 masl), and 0.74 atm (2600 masl). The simulations used an axisymmetric 2D geometry of the system in steady state, where the heat exchanger of the self-recuperative burner was considered. It was found that the Eddy dissipation concept (EDC) model, associated with a reduced mechanism, presented good results for temperature and species concentration with low computational time. Two cases were compared: one maintained the fuel, combustion air, and ejection air mass flows constant at sea-level operation values with changing atmospheric pressures, referred to as the corrected case, while the other, not-corrected case, allowed the mass flows to vary as a result of changes in auxiliary performance with the atmospheric pressure. 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 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.