We investigate the processes of growth and consumption of rifted stratovolcanoes to better understand their morphostructural and geological evolution in relation to sheet intrusions. Field data collected from four rifted volcanoes, located in Italy and Chile, and representing structural end members, are integrated with scaled physical models and numerical three-dimensional (3D) modeling. Due to preferential along-rift magma pathways, volcanoes grow perpendicular to rift strike mostly by intrusions, and parallel to the rift mostly by effusions. These constructive processes are partially or fully balanced by destructive processes that occur both perpendicular to the rift and along the rift zone, and that are initiated by the sheet intrusions. Field data indicate that sheets and/or flank eruptions increase in number approaching the summit part of a cone. Since dyking within a volcano causes a magmatic driving overpressure and lateral displacement/deformation of the cone flank, this displacement is assumed to be greater where intrusions have the highest frequency. Lateral deformation can also lead to flank failure along a deep-seated slip surface. Symmetrical rifts may produce deep-seated collapses in opposing directions, while asymmetrical rifts can preferentially lead to destruction on the tectonically downthrown side. If the collapse depression is refilled by new volcanism, the cone attains a new critical height (and mass), setting the scene for renewed failure. This sequence inhibits the cone from widening normal to the rift zone. The field examples studied, plus analog and numerical modeling, also indicate that dyking within the rift zone destabilizes the volcano flanks along the rift: where dyke tip stresses approach the slope, surface landsliding might be induced. This in turn produces debuttressing above the dyke, favoring effusive eruptions and lavas flowing within the landslide depression. In this case a balance can occur between new lava outpourings and gravity mass removal, or the volcano can grow along the rift if the emitted magma volume is higher than the collapsed material. From a mechanical point of view, the different behavior of volcanic slopes, both parallel to and perpendicular to dyke strike, is a function of magma forces and the cumulative dyke-induced displacement. The combination of along-rift-strike landsliding and normal-to-rift deep-seated large-scale lateral collapse, characteristically produces in map view four main zones of “consumption” and “rebuilding” on the volcano. These alternate with four triangular sectors where the volcano slopes are relatively more stable. When volcanic activity ends, cone consumption is concentrated along the rift and is favored by fault slip or channeled erosion.