Masonry arch bridges, which were generally built using brick and stone materials, still form a significant part of the highway and railway networks in the World. The subsoil deformability may considerably affect seismic damage mechanics of masonry arch bridges. The paper investigates the effects of nonlinear foundation soil behavior on the seismic damage mechanisms of brick and stone semicircular masonry arch bridges. Direct soil-structure interaction (SSI) approach is taken into account in the 3 D finite element models of the masonry arch bridge-foundation-soil interaction systems including contact, finite and infinite elements. Nonlinear behaviors of masonry units and homogenous soil domain are modeled using the Concrete Damage Plasticity (CDP) and Mohr-Coulomb failure criteria. The selected ground motion is matched and deconvoluted for hard and medium soil domains. Seismic damage mechanisms of brick and stone masonry arch bridges subjected to combined longitudinal and vertical deconvolved ground motion components are obtained for hard, medium, and partially hard and medium soil domains and are compared with each other.