A study on the ultimate span of a concrete-filled steel tube (CFST) arch bridge investigates the influence of parameters such as pipe diameter, wall thickness, and cross-section height on the bridge's ultimate span. Using finite element analysis and the response surface method, the study determines the optimal parameters that maximize the span while meeting structural strength, stiffness, and stability constraints. The results show that the ultimate span increases with pipe diameter, wall thickness, and cross-section height, but eventually decreases due to material stress limits. The optimal parameters for the ultimate span of 821 m are a pipe diameter of 1.49 m, wall thickness of 37 mm, and cross-section height of 17 m, with an arch axial coefficient of 1.2. The study also verifies the results using finite element analysis, confirming that the structural strength, stiffness, and stability meet the required limits. The response surface method significantly improves the efficiency of determining the ultimate span by reducing computational workload and providing a mathematical model for optimization. The findings contribute to the understanding of CFST arch bridge design and highlight the potential for larger spans in future bridge construction.A study on the ultimate span of a concrete-filled steel tube (CFST) arch bridge investigates the influence of parameters such as pipe diameter, wall thickness, and cross-section height on the bridge's ultimate span. Using finite element analysis and the response surface method, the study determines the optimal parameters that maximize the span while meeting structural strength, stiffness, and stability constraints. The results show that the ultimate span increases with pipe diameter, wall thickness, and cross-section height, but eventually decreases due to material stress limits. The optimal parameters for the ultimate span of 821 m are a pipe diameter of 1.49 m, wall thickness of 37 mm, and cross-section height of 17 m, with an arch axial coefficient of 1.2. The study also verifies the results using finite element analysis, confirming that the structural strength, stiffness, and stability meet the required limits. The response surface method significantly improves the efficiency of determining the ultimate span by reducing computational workload and providing a mathematical model for optimization. The findings contribute to the understanding of CFST arch bridge design and highlight the potential for larger spans in future bridge construction.