By means of a spherical Earth model with Maxwell rheology, an analysis of the postseismic deformation field due to the viscoelastic relaxation of the mantle and asthenosphere following the great 1960 Chile earthquake is performed. Due to the exceptional energy release of that earthquake, geomorphological evidences of postseismic deformation are available in a broad area surrounding the rupture zone. The comparison of the synthetic results with the available data allows to put some constraints on the viscosity of the asthenosphere beneath the Chilean region. Values between 8⋅1019 and 1020 Pa s are compatible with the available postseismic deformation field data. ¿ 1999 American Geophysical Union