By means of a finite element algorithm we investigate the effects of lateral viscosity variations upon the horizontal motions currently detected by VLBI techniques in Europe. Our axisymmetric flat models, appropriate to describe the rebound due to the melting of the Fennoscandia ice-sheet, are characterized by a layered compressible mantle with linear Maxwell rheology. We have first computed the time-evolution of theoretical baselines characterized by a simple geometry. In agreement with previous results, the rates of horizontal deformation have been found to be greatly sensitive to both lateral viscosity variations and deep mantle stratification, especially for baselines located in the vicinity of the ice sheet margin. To complete our study, we have compared our numerical results with the observed time-evolutions of relevant European baselines. Onsala-Wettzell and Onsala-Eflsberg are fitted by a laterally varying asthenosphere and sharp viscosity increase in the lower mantle; longer baselines, connecting these sites to Medicina (northern Italy), indicate that post glacial rebound is responsible only for a fraction of the VLBI observations, the residual being thus attributable to continental collision in the Mediterranean Sea.¿ 1997 American Geophysical Union