In the Central Andes, crustal thickness is not well correlated to upper crustal shortening. Only little shortening is documented in the upper crust of the 60--65 km-thick Altiplano plateau, whose thickening and uplift were delayed with respect to earlier and greater thickening in the adjacent Western and Eastern Cordilleras. Because crustal thickness variations induce horizontal stress gradients and cause crustal flow, a thickness-dependent channel flow is modeled here and applied to the Central Andes. In situ thickening is assumed for both cordilleras, while the Altiplano crustal thickening is generated by lateral flow from these overthickened adjacent domains. A ~8.1018 Pa s viscosity channel is predicted for crustal thicknesses exceeding 45--50 km to match the estimated topographic evolution of the Central Andes. Thickening in the cordilleras was sufficient to generate a flow of 6.109 m3 per unit length toward the initially ~30--35 km-thick Altiplano.