GPS observations in south Iceland between 1994 and 2003 are compared with two-dimensional elastic half-space and viscoelastic coupling models for two parallel rift zones, representing the Western and Eastern volcanic zones (WVZ, EVZ). GPS data from the Hreppar block, between the WVZ and EVZ, fit a rigid block model within uncertainties. Spreading rates across the WVZ increase from 2.6 ¿ 0.9 mm/yr in the northeast to 7.0 ¿ 0.4 mm/yr in the southwest. Conversely, spreading rates in the EVZ decrease from 19.0 ¿ 2.0 mm/yr in the northeast to 11.0 ¿ 0.8 mm/yr in the southwest, the direction of ridge propagation. Summed extension rates across the two rift zones are approximately constant and equal to the total plate rate, ~18--20 mm/yr, consistent with a simple propagating ridge model whereby the WVZ is deactivating in the direction of EVZ propagation. The coupling model confirms results from the simple elastic half-space model, including relatively shallow locking depths (<5 km) beneath the rift zones, and allows for an estimate of mean viscosity (~1019--1020 Pa s) beneath the elastic layer. The location of maximum surface velocity gradient in the EVZ, presumably the locus of subsurface magma accumulation and future rifting, does not coincide with the 1783--1784 Lakag¿gar fissure eruption but is 20 km to the west, on the B¿r¿abunga-Veidiv¿tn fissure swarm. This had a small volume eruption in 1862--1864 but a major eruption in 1477 A.D.