Large polygenetic volcanic edifices grow through the accumulation of internal and external accumulation of magmatic and volcanic products [Annen et al., 2001]. The internal stress state of a volcanic edifice and its superficial faulting are complex and relate to its geological history. The formation of a large volcano loads the underlying lithospheric plate and can lead to lithospheric flexure and faulting. In turn, lithospheric deformation affects the stress field beneath and within the volcanic edifice and can influence magma transport [Thurber and Gripp, 1988; McGovern and Solomon, 1993], and favor their spreading over soft materials [Borgia et al., 1992]. Modeling the interaction of these processes is crucial to understand the history of eruption characteristics and tectonic deformation of large volcanoes.