The arch stone bridge, known as the Podgradska ćuprija, located over the Bregava River in Stolac, Bosnia and Herzegovina, is a significant historical structure that has stood the test of time. Stone arch bridges, known for their durability and architectural significance, require continuous evaluation to maintain their structural integrity, particularly in the face of increased traffic loads and environmental degradation. This case study aims to analyze the structural integrity of the bridge using the RING 3.2 software, a comprehensive tool for evaluating the behavior of masonry arch structures, to assess the bridge’s load-bearing capacity and failure mechanisms. The historical and engineering characteristics of the bridge are examined, including material composition, geometric configuration, and the effects of past modifications. The findings indicate that while the bridge remains structurally stable under moderate loading conditions, certain strengthening may be required to ensure its long-term functionality. The research contributes to the broader field of heritage preservation by demonstrating effective methodologies for assessing and maintaining historic masonry structures.