The Andes, the world's second highest orogenic belt, were generated by the Cenozoic tectonic shortening of the South American plate margin overriding the subducting Nazca plate. We use a coupled thermomechanical numerical modeling technique to identify factors controlling the intensity of the tectonic shortening. From the modeling, we infer that the most important factor was accelerated westward drift of the South American plate; changes in the subduction rate were less important. Other important factors are crustal structure of the overriding plate and shear coupling at the plates' interface. The model with a thick (40–45 km at 30 Ma) South American crust and relatively high friction coefficient (0.05) at the Nazca–South American interface generates >300 km of tectonic shortening during 30–35 m.y. and replicates the crustal structure and evolution of the high central Andes. The model with an initially thinner (<40 km) continental crust and lower friction coefficient (<0.015) results in <40 km of South American plate shortening, replicating the situation in the southern Andes. Our modeling also demonstrates the important role of the processes leading to mechanical weakening of the overriding plate during tectonic shortening, such as lithospheric delamination, triggered by the gabbro-eclogite transformation in the thickened continental lower crust, and mechanical failure of the sediment cover at the shield margin.