In the past 50 years, many long-span continuous stone arch bridges have been built in China. Analysis of mechanical performances and load capacities of long-span continuous stone arch bridges has important significances for the safety assessment of the similar bridges. 3D elastoplastic finite element method is employed to analyze ultimate bearing capacity of a three-span arch bridge with sandstone masonry in this paper. The characteristics of structural geometric and material nonlinearities and cracking and crushing of the masonry are taken into account. Compared with single-span arch bridge, both the coaction of spandrel structure and main arch and the influence of loading arrangements on ultimate bearing capacity is analyzed. The failure characteristics of the structure under the ultimate load are also introduced. The analysis results and conclusions can be referenced for the safety assessment of similar bridges.