We perform numerical modeling to investigate the mechanisms leading to the postcollisional tectonic evolution of the Alps. We model the lithospheric deformation as a viscous thin sheet with vertically averaged rheology and coupled with surface mass transport. The applied kinematic boundary conditions simulate the convergence between the Adria indenter and the European foreland during the last 35 Myr. Model predictions of elevation, lithospheric structure, erosion/sedimentation pattern and vertical axis rotation are compared with observations of the planform shape of the chain, topography, crustal thickness, distribution of rock exhumation and sediment thickness, and paleomagnetic rotations. Thickening of the lithosphere in the Alpine region is shown to be highly sensitive to the assumed viscosity law, to the strength contrasts between the different regions and to the surface mass transport. Modeling results indicate that the large-scale deformation of the Alps during the postcollisional phase is mainly controlled by accommodation of convergence in a weak orogenic zone caught between a nearly rigid Adria plate and a strong European foreland. Modeling of the present-day stress field shows that (1) the present rotation of Adria is responsible for the change of extension direction from strike-perpendicular in the western Alps to strike-parallel in the east and (2) the strike-perpendicular extension observed in the western Alps is likely due to lateral variations of gravitational potential energy. The results suggest a NNE shift of about 700 km of the Euler pole of Adria relative to Europe from its mean position during postcollisional deformation to the present day. Copyright 2005 by the American Geophysical Union.