Masonry arch bridges, which essentially form a significant part of our historic infrastructure, are constantly challenged by independent and a combination of hazard scenarios. Even though studies have quantified the behaviour of arch bridges subjected to independent structural demands, very few studies have considered the performance of these structures considering multiple structural demands. In this context, an analytical procedure is developed for masonry arches considering the interaction of support settlement and horizontal seismic forces. The adopted analysis procedure based on kinematic analysis utilizes an iterative algorithm to quantify the collapse of the arch. Linear and nonlinear kinematic frameworks are formulated to evaluate the bridge performance under the compound structural demands, which is validated against a numerical model. The proposed method provided key insights into the interaction between the collapse mechanisms initiated by support translation and seismic demand and their effect on the arch capacity.