The thermal safety characteristics of the system after a small break loss of coolant accident (SB-LOCA) in a helium xenon gas-cooled small reactor will determine whether the reactor will experience a meltdown and the duration of the meltdown. At present, research on SB-LOCA both domestically and internationally is mostly focused on water-cooled reactors, lacking relevant research on helium xenon gas-cooled reactors (He-Xe GCR). Therefore, it is of great significance to research the thermal safety characteristics of He-Xe GCR after a breach loss of coolant accident. This article improves the gas turbine model based on the original SB-LOCA analysis program for pressurized water reactors. And added a calculation model for the characteristics of helium xenon mixed gas, a heat transfer model for helium xenon mixed airflow, and a compressor model. Finally, a Brayton Cycle Reactor System Analysis program (BRESA) was developed for SB-LOCA analysis of He-Xe GCR. Explore the impact of the size and location of fractures on the thermal safety characteristics of the system using BRESA. Research has found that as the size of the rupture gradually increases, the decrease in reactor core power is greater, and the reactor power is shut down earlier. Comparative analysis of the impact of different breach positions on the residual heat removal characteristics reveals that a breach accident on the high-pressure side of the system poses a greater threat to system safety. Therefore, when setting the safety threshold for the Brayton cycle system, the focus should be on the hazards of high-voltage side breaches. This research achievement assists with the safe operation strategy of He-Xe GCR in the future.