The process of failure propagation of masonry buildings during earthquakes is simulated using a refined version of the distinct element method that simulates three-dimensional elastic, failure, and collapse behaviors of structures. Models with a flat roof and models with a vault roof are considered, and their failure propagation mechanisms are examined. The influence of the direction of the input ground motion on failure propagation is also investigated. Moreover, the effectiveness of three reinforcement measures is compared. One measure is increasing the mortar strength, the second is increasing the thickness of the bearing walls, and the third is introducing wooden columns and beams. Among these measures, increasing the mortar strength is found to be the most effective. Increasing the thickness of the bearing walls and introducing wooden columns and beams are found to be effective only if the roof has sufficient integrity since the collapse of the roof depends on the integrity of the bearing walls and the roof itself.