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The stereotomy (bricklaying pattern) of masonry arches is not only a characteristic of the architecture of these structures, but also an important revealing element of mechanical safety when degradations appear in the complex material of masonry. This paper presents the effect of randomness of this parameter on the bearing capacity of masonry arch bridges based on reliability of structures. Different mechanical models that are classically used for the analysis of the bearing capacity of masonry arches can support a reliability analysis. In this paper, a rigid block model and finite-element model are presented and compared. Then, focusing on the rigid block method, stereotomy has been integrated as a geometrical parameter influencing the mechanical behavior. To this end, the stereotomy function is presented as a parameter that can be influenced by the possible degradations affecting the blocks and/or mortar joints, thus justifying its randomness and consequently integrating it in a reliability study. The reliability study carried out in this work focused on the case of a single-span masonry arch bridge located in Morocco. The reliability analysis demonstrated the importance of joints orientation and the possible perturbations that it can undergo around the classical radial configuration. The effect of these perturbations is shown for the failure multiplier, which represents the bearing capacity of the studied arch. Masonry arch bridges are a heritage of great architectural and economic importance for many countries worldwide. This is due to the historical value of these ancient constructions, but also to their durability that allowed them to still fulfil their economic role. Nevertheless, the preservation of the safety of masonry arch bridges depends on a good maintenance approach that takes into account the different hazards affecting these constructions. The uncertainties affecting the geometry are among the hazards to be taken into account by the roadway and railway managers. In this paper, the authors study the effects of uncertainties related to the bricklaying pattern of masonry blocks on the mechanical behavior of the arch bridge. For this purpose, probability-based methods are applied in conjunction with mechanical calculation techniques. The results obtained highlight the importance of considering the stereotomy parameter, which represents the bricklaying pattern of masonry blocks in the arch in maintenance operations. [ABSTRACT FROM AUTHOR]