The Central Andes (~21°S) is a subduction-type orogeny formed in the last ~50 Ma from the subduction of the Nazca oceanic plate beneath the South American continental plate. However, the most important phases of deformation occur in the last 20 Ma. Pulses of shortening have led to the sudden growth of the by the Altiplano-Puna plateau. Previous studies have provided insights on the importance of various mechanisms on the overall shortening such as the weakening of the overriding plate from crustal eclogitization and delamination, or the importance of a relatively high friction at the subduction interface, and weak sediments in foreland. However none of them has addressed the mechanism behind these shortening pulses yet. Therefore, we built a series of high resolution 2D visco-plastic subduction models using the ASPECT geodynamic code, in which the oceanic plate is buoyancy-driven and the velocity of the continent is prescribed. We have also implemented a realistic geometry for the south American plate at ~30 Ma. We propose a new plausible mechanism (buckling and steepening of the slab) as the cause of these pulses. The buckling leads to the blockage of the trench. Consequently, the difference of velocity between the South American plate and the trench is accommodated by shortening. The data presented here includes the parameters files, for the reference model (S1) and the following alternative simulations: models with variation of the friction at the subduction interface (S2a-c), a model without eclogitization of the lower crust (S3) and a model with higher thermal conductivity of the upper crust (S4). Additionally, this publication includes the initial composition and thermal state of the lithosphere used for the models and a Readme file that gives all the instructions to run them.