The Chapter revisits classic analytical approaches based on equilibrium and admissibility to assess the stability of masonry arches and vaults. A particular focus is given to Durand-Claye’s method and its modern re-interpretations developed in recent years. Durand-Claye proposed an original graphical method for assessing the stability of masonry arches and vaults. The procedure proposed by Durand-Claye is aimed at determining all the thrusts that allow for verifying the equilibrium of any given part of the arch and are at the same time compatible with the masonry strength, by drawing a particular plane figure, the stability area. In 1880 Durand-Claye extended his stability area method to assess the equilibrium of domes of revolution. The Ch...