Controversy has existed over whether or not viscous relaxation is an important process on the icy satellites. Previous models involve large extrapolations of Newtonian flow laws for ice, whereas ice is known to exhibit non-Newtonian behavior. Recently, the flow law parameters for ice at the appropriate temperatures and stresses have been measured. Numerical modelling of the viscous relaxation of basins in Ganymede using these parameters has given implausibly short relaxation times. However, this model treated ice as a purely viscous substance, so that no elastic lithosphere could develop near the surface. Here we treat ice as a Maxwell visco-elastic material and numerically model the relaxation of basins on Ganymede. We find that realistic Young's moduli lead to little relaxation occurring in basins even 4.0 Ga after their formation. Further, we demonstrate that within broad limits the near surface temperature gradient has little effect on this result. Finally, through examination of the distribution of Maxwell times in the vicinity of the crater, we show that most viscous relaxation occurs early in the basin's history when stresses are high, and thus Maxwell time is short. As stresses are relieved, the Maxwell time becomes long, and relaxation essentially ceases. ¿ American Geophysical Union 1989