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We implement an analytical model based on flexural deflection of a thin elastic disc to investigate the magnitude of lithospheric decompression caused by deglaciation at upper crustal magmatic reservoirs. Considering a published numerical climate model describing the space-time evolution of deglaciation after the Last Glacial Maximum (LGM) along the Southern Volcanic Zone (SVZ) of the Andes, we demonstrate that changes in pressure at upper crustal levels (<10 km depth) at the scale of several hundred years are of the order of 10-100 MPa. Total decompression and decompression rate (300-150 kPa yr(-1)) are 1-2 orders of magnitude larger than values previously estimated by other authors who assume that glacial loads are supported by an elastic half-space, that is, of infinite elastic thickness. The large decompression caused by flexural unbending of an elastic plate of finite thickness as assumed here can easily surpass the tensile strength of rocks (5-20 MPa), creating adequate conditions for failure of the reservoir walls, dike propagation inside and outside the reservoir and the eventual collapse of the reservoir accompanying an explosive eruption. We apply our results to the analysis of post-glacial eruptions of SVZ volcanoes, which erupted large volumes (>10 km(3)) of mafic ignimbrites hundreds to thousands of years after deglaciation onset. We show that this time lag is necessary to achieve a decompression of several tens of megapascals at depths of several kilometres that are consistent with the location of magmatic reservoirs as estimated by independent petrologic, seismic and/or geodetic studies. Moreover the northward increase of this time lag is in agreement with a smaller size of the Andean ice cap in the north than in the south during the LGM. For wet, volatile-rich magmas typical of subduction zones, the effect of large decompression at upper crustal reservoirs caused by flexural unbending of the lithosphere after deglaciation could play a major role in promoting large explosive eruptions through devolatization of the magma, during past deglaciation events as demonstrated here for the LGM along the SVZ and current accelerated ice retreat caused by climate change over large segments of subduction-related arcs at higher latitudes.