In this chapter fundamentals of graphical statics are recalled in order to introduce those techniques (Méry, Durand-Claye, Eddy, Lévy, Wolfe) that inspired modern computerized versions for the equilibrium analysis of masonry arches and domes. The historical contributions are critically examined, by highlighting their application potential. Particular emphasis is given to the Durand-Claye method, a graphical procedure able to check the existence of admissible solutions by taking into account the compressive strength of masonry. Applications to masonry mechanics issues and on historic structures are finally shown