A study on the 2D and 3D modeling of the Osserain Bridge’s capacity estimation and failure mechanisms is presented. The study investigates the bridge’s response to specific loading scenarios, both with and without the fill layer, and simulates its demolition, which was carried out in early 2023. This is accomplished using the in-house tool Gavrinis, which applies the framework of limit analysis to rigid-block discrete masonry, enabling the consideration of masonry anisotropy and the management of unavailability of historical data. The tool allows for modeling various failure mechanisms at the joint level, such as sliding, rocking, and crushing. Both associative and non-associative flow rule calculations are performed in this study. The results provide insights into the structural behavior of the Osserain Bridge, offering a comprehensive understanding of its failure modes. The findings also demonstrate the tool’s effectiveness in simulating masonry structures’ stability and failure, which can contribute to enhancing the safety and management of existing masonry bridges.