Abstract In this study, lateral capacity and load-deflection behavior of unreinforced stone masonry walls are analyzed based on the discrete element method considering the uncertainties in the material properties. Through this research, discontinuum-based computational models are used to simulate the composite and low-bond strength characteristics of masonry. The unreinforced masonry walls are replicated via the system of deformable rectangular blocks interacting along their boundaries. Local failure modes of masonry (cracking, sliding, and crushing) are taken into consideration at the joints, in which the contact stresses are calculated and updated based on the relative displacement among the adjacent blocks and contact constitutive models, respectively. First, the numerical approach is experimentally validated using previous test results. The same models are then used to determine the influence of uncertainties in the material properties on the macro behavior of the URM walls. The importance of considering the inherent variability in the material and modeling parameters is highlighted. Results clearly show the informative outcomes of the stochastic analysis and provide a deeper understanding of the structural behavior of URM walls in terms of the governing failure mechanisms, displacements, and load-carrying capacities. These results also underline the importance of the variability in the force and displacement capacities, which should be considered when defining performance limits for stone masonry in the future, as they are currently unavailable in national standards for Turkey and the US.