Substantial part of heritage structures in Turkey is historic masonry arch bridges. To explore modeling issues, a numerical work has been initiated to better understand and preserve/transfer this heritage to the next eras. This paper specifically describes the influence of tensile fracture energy of stone material in determining their true load carrying capacities. A case study is presented to explain the modeling issues. With its historical background, current situation, geometric and material properties, this work focuses on numerical investigation of the historic multi-span stone masonry arch Justinian’s (or Sangarius) Bridge located in the city of Sakarya in Turkey over the Sakarya River. Numerical results show that the value of fracture energy in tension significantly affect the load carrying capacity and failure mechanism of multi-span masonry arch bridges. A more realistic nonlinear response has been obtained for an upper value of the tensile fracture energy of the stone masonry. The bridge model collapses by a-three-hinge mechanism occuring at the loaded arch in the upper value of the tensile fracture energy. The most critical loading point of the bridge is determined as the quarter-span.