The April 29, 1991 Racha, Georgia Mw=6.9 earthquake was the largest earthquake recorded in the western section of the Greater Caucasus Mountains. Lithospheric deformation following this earthquake was recorded by a network of eight GPS stations. These data were modeled for postseismic deformation with the mechanisms of afterslip and viscoelastic relaxation. Prior to modeling, the GPS data were corrected for secular tectonic motions by two separate methods. The first was to use the 1996-2000 portion of the GPS time-series as an estimate of preseismic deformation rates. The second method involved using a regional tectonic block model to produce velocity estimates for the GPS stations. Shallow afterslip was found to best explain the data for the 1991-1994 time period with a moment of 7 x 10¹⁸⁴ N m. This is equivalent to about 20% of the coseismic moment and represents 300 times the total moment released from aftershocks during the same time period. Most of the postseismic deformation was completed by 1994. While viscoelastic relaxation was not found to be responsible for postseismic deformation, it was determined that viscosities less than 10¹⁸ Pa sec can be ruled out for possible a possible viscoelastic layer in the lower crust.