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. Key Points Explanation for the geodetic uplift of the Alps Revisit the relation between deglaciation and uplift Pointing out the key role of rheology on strain