158The study of masonry structures has fascinated architects, geometers, and engineers since antiquity. Artifacts like the Pantheon in Rome and Gothic cathedrals, which have stood for centuries without the benefit of modern mechanical engineering and materials science research, stand testament to the power and elegance of masonry construction techniques. This chapter sketches how the mechanics of masonry structures, and smooth and discrete geometry, are inseparably entwined, beginning with a historical overview of how stable structures were designed, covering some fundamental theory, and then surveying recent works in computer graphics on computational design and analysis of masonry structures. Weight functions defining generalized barycentric coordinates appear as a key component of this analysis, where they represent the force flowing through the structure.