Since the late Miocene, the two main segments of the central Andean high plateau, Altiplano and Puna, demonstrate different styles and magnitudes of tectonic shortening. Through numerical simulation of thermomechanical processes, we show that different shortening modes—pure and simple shear accompanied by thin-or thick-skinned tectonics—might be controlled by strength of the foreland uppermost crust and by temperature of the foreland lithosphere. Mechanical weakening and failure of the thick Paleozoic sediments overlying the cold lithosphere in the Altiplano foreland at 13–9 Ma explains the transition from pure to simple shear shortening accompanied by broad thin-skinned thrusting, started before the major uplift of the plateau. However, the high strength of the uppermost crust combined with a relatively warm lithosphere results in the thick-skinned shortening typical for the foreland of the Puna. Failure of Paleozoic sediments in the Altiplano foreland significantly reduces the force required to shorten the lithosphere, which may be the reason for the increased bulk shortening rate in the late Miocene.