More than 10 years of geodetic measurements demonstrate an uplift rate of 1–3 mm/yr of the high topography region of the Western Alps. By contrast, no significant horizontal motion has been detected. Two uplift mechanisms have been proposed: (1) the isostatic response to denudation responsible for only a fraction of the observed uplift and (2) the rebound induced by the Wurmian ice cap melting which predicts a broader uplifting region than the one evidenced by geodetic observations. Using a numerical model to fit the geodetic data, we show that a crustal viscosity contrast between the foreland and the central part of the Alps, the latter being weaker with a viscosity of 1021 Pa s, is needed. The vertical rates are enhanced if the strong uppermost mantle beneath the Moho is interrupted across the Alps, therefore allowing a weak vertical rheological anomaly over the entire lithosphere.