The central Andes form a wide elevated plateau flanked in the west by a steep slope toward the deep Chilean Trench and in the east by a gentle slope that subsides gradually toward the Brazilian Shield. The low elevated trench topography is dynamically supported, whereas the high Andean mountain topography is mostly isostatically supported by a thick crust. The last mountain building phase, which thickened the crust and formed the present-day Andes, began 26 m.y. ago, in the late Oligocene, with the increase of the convergence rate between the Nazca and the South American plates. We investigate the time evolution of the Andean deformation and topography by applying a temperature dependent viscoplastic flow model of continental lithosphere to the South American plate. The model predicts the observed present-day topographic profile across the central Andes, from the trench across the high Altiplano plateau to the Brazilian Shield. Our numerical results, combined with observations of the spatial and temporal distribution of igneous activity in the central Andes, lead us to conclude that the Altiplano developed and extended to its present width of 400 km as a result of thermal weakening of the lithosphere since late Oligocene until present. The model also predicts the observed eastward migration of the locus of the Andean crustal deformation with time. At early stages, both the crustal and mantle loci of deformation lie in the thermally weak region, which results in crustal thickening in this finite region. At later stages, as the crust thickens, it induces increased buoyancy forces, which resist crustal thickening beyond 65 km. As a result, the locus of crustal deformation migrates eastward. The detachment of the crustal locus of deformation from that of the mantle can explain the observed change in deformation pattern from thick-skinned tectonism during early stages of the deformation to thin-skinned tectonism during the more recent stages.