During the Weichselian glaciation Iceland was covered with an ice cap which caused downward flexure of the Earth' surface. The post-glacial rebound in icleand was very rapid, being completed in about 1000 years. The length of this time interval constrains the maximum value of asthenosphere viscosity in Iceland to be 1¿1019 Pa s or less. Further clarification of the ice retreat and uplift history may reveal lower viscosity. Current changes in the mass balance of Icelandic glaciers must lead to measurable elevation changes considering this low viscosity. Expected current elevation changes around the Vatnaj¿kull ice cap are of the order of 1 cm per year, due to mass balance change in this century. ¿American Geophysical Union 1991