Current plate tectonic reconstruction theory needs to begin to confront the challenges associated with modelling penetrative deformation of the continents. The model presented here is the compilation of numerous palaeogeographic models and various geochronological, geological and geophysical data within a deformable, mesh-based framework. While there are competing interpretations for Andean evolution, particularly regarding the formation of the Bolivian Orocline, this deformable model of Cretaceous to present Andean evolution demonstrates several interesting implications in terms in terms of strain, topography, geometry and relative translations. Our model presents that the Central and Southern Andes formed a sub-linear belt during the Cretaceous. After a period of large-scale extension in the Jurassic, crustal shortening associated with Rocas Verdes Basin closure produced the Patagonian Orocline. In the Central Andes we have assumed that both differential shortening and crustal block rotation, from the Mid-Eocene to present, formed the Bolivian Orocline. Crustal growth has occurred in the Northern Andes by means of episodic terrane accretion throughout the Mesozoic-Cenozoic. This study was developed within the Pplates mesh-based software, allowing us to quantify the implications of the model through assessable predictions. However, there are several other geodynamic explanations that may fit the data utilised here. Thus the next step would be to test alternative palaeogeographic models and datasets, and see how these compare to the model presented here, specifically in terms of the evolution of individual Andean basins, tectonic block rotations, terrane accretions, and subduction zone dynamics. This could easily be achieved with use of the Pplates software, and such models could be updated as new or additional data are evaluated. Such an approach is required if we are to overcome the problem associated with modelling and testing the fluid-like evolution of Earth's orogenic zones.