The relatively low elevation and thick crust in the Altiplano, in comparison to the higher elevation, but thinner crust in the Puna plateau, together with geophysical data, suggest that isostatic equillibrium is achieved by cooler and denser lithospheric mantle in the Altiplano. Excess density in the Altiplano mantle could create differential horizontal stress in the order of 25 MPa between both lithospheric columns. Numerical models accounting for pressure and temperature-dependent rheology show that such stress can induce horizontal ductile flow in the lower crust, from the Puna towards the Altiplano. With a minimum viscosity of 1019Pa.s, this flow reaches 1 cm/yr, displacing more than 50 km of material within 5 Ma. If the lower crust viscosity is smaller, the amount of orogeny-parallel lower crustal flow can be even greater. Such a mechanism of channel flow may explain that different amounts of crustal material have been accomodated by shortening in the Altiplano and in the Puna. Because of the strength of the - brittle - upper crust, this channel flow does not necessitate large amounts of suface deformation (except vertical uplift), making it difficult to detect from the geology.