Large volcanic edifices constitute enormous loads at the surfaces of planets. The lithosphere, the mechanically strong outer layer of a planet, responds to growing edifice loads by flexing. The shape of this lithospheric flexure and the resulting stress state exert critical influences on the structure of the evolving edifices, which in turn feed back into the flexural response. Flexural subsidence of the lithosphere forms topographical moats surrounding volcanoes that are partially to completely filled by landslide debris, volcaniclastic materials and sediments, or by relatively flat aprons of volcanic flows. Flexure creates a characteristic ‘dipole’ state of stress that influences subsequent magma ascent paths and chamber dynamics in the lithosphere. Compression in the upper lithosphere can inhibit magma ascent and favour the development of oblate magma chambers or sill complexes. This compression can be transferred into the edifice unless a décollement allows the volcano base to slip over the underlying lithosphere; generally, basal décollements are found to operate via high pore-fluid pressure in a clay sediment-based layer. Volcanoes lacking such a layer, regardless of the thickness of the basal sediments, lack basal décollements and, thus, tend to be limited in size by compressive stresses adverse to magma ascent.