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Volcanoes in extensional environments may show gradual subsidence over decades during quiescent periods, due to various processes such as magma withdrawal, cooling, contraction, plate spreading and viscoelastic response. If significant rheological anomalies reside in volcano roots, due to the presence of magma and hot rock, they can influence the style of deformation. We use Finite Element Method (FEM) models to explore how strain localization due to extension can lead to volcano deflation. We apply rheological models comprising an elastic layer overlying a viscoelastic domain and include local up‐doming regions of low viscosity material beneath volcanic centers. The models reveal a localized subsidence above the rheological anomaly, influenced by the tectonic extension, and by the up‐doming volume and its viscosity. The models suggest that plate divergence may account for 4–5 mm/yr of observed subsidence at Krafla and Askja volcanic systems (KVS and AVS, respectively) in North Iceland. Plain Language Summary: Extensional stretching may have an important effect on the ground deformation observed at volcanic systems located along a divergent boundary. The physical properties of the crust are altered by the presence of hot material and/or geothermal activity at central volcanoes, compared to the surrounding rocks. We use a two‐layer model consisting of an elastic crustal volume overlying a viscoelastic layer, which locally reaches shallower depth (referred to up‐doming material), to investigate such crustal properties beneath volcanic systems. We explore a wide range of viscosity values in the up‐doming material and elastic layer thickness. The models, applied to investigate observed ground deformation at the Krafla and Askja volcanic systems, suggests that regional stretching with realistic material properties in the crust beneath the volcanic system, fits quite well the observed deformation satellite data at Krafla volcanic system in the 2015–2018 observations, but only a minor contributor to the Askja deformation pattern in the same period. Our modeling approach suggests that any extensive magmatic system undergoing stretching should feature subsidence in relation to the presence of hot material/magma mush beneath volcanic systems. Key Points: Gradual deflation (mm to cm per year) over decades has been observed at the Krafla and Askja volcanic systems in IcelandNumerical models show that deflation is induced by stretching across volcanic systems and dependent on their crustal rheological anomaliesFor the 2015–2018 period, an extensional model can broadly explain observed deflation at Krafla, but only ∼25%−30% at the Askja caldera [ABSTRACT FROM AUTHOR]