Plate coupling between oceanic and continental plates in convergent margins of Andean type is analyzed from the continuum mechanics approach. We postulate a simple mechanism that accounts for the compressive regime in Andean-type environments. In this mechanism, deformation in the continental lithosphere is split into two distinctive domains: The forearc domain and the arc-foreland domain. The forearc deformation is controlled by the balance between buoyancy forces associated with the trench and continental slope relief and the stress transferred from the convergence velocity through the age- and velocity-dependent slip zone. The arc-foreland deformation is controlled by the absolute plate velocity of the continental plate and the resistance at the slip zone. Strength of the coupling zone is determined by analyzing the dynamic trench topography along the active margin of South America between 0 and 55¿S. Using this approach, we found strength values in the range of 20--95 MPa, in strong direct correlation with the age of the subducting plate. The slip layer strength observation has been successfully tested against a thermal- and strain rate-dependent rheological model. From this theoretical result we define an empirical relationship between strength of the slip zone and the age and convergence velocity. Applying this plate coupling model, we reproduce shortening rates in the order of 1--10 km/Myr, in agreement with those reported for the late Tertiary evolution of the Andes. Model results reproduce some first-order features of the geological evolution of the margin, such as the shape of the trench, the overall Andes relief, the Altiplano buildup, and block rotation patterns. In addition, the model provides a mechanism to explain the evolution of the Central Depression, the inversion of Tertiary basins under slow convergence rates during the Miocene, and the segmentation of the margins tectonic erosion.