Geodetic observations of horizontal and vertical point displacements in a ~100-km-wide network across the Krafla fissure swarm of NE Iceland are analyzed with simple elastic models. The observed displacements accumulated from 1975 to 1980 in several events of magma injection into fissures that were widened. The fissure swarm was extended, and it subsided while the adjacent lithosphere contracted or was compressed accompanied by surface uplift. We applied two models to fit the far-field deformation: an infinite horizontal pressure line source or a pipe and an infinite, vertically limited, vertical dyke source loaded by normal stress at the walls, both embedded in an elastic half-space. In the far-field inversion the two models cannot be distinguished, but geology and the observed axial graben subsidence clearly discriminate against the pipe and for the dyke. The inversion suggests that the widened dykes cut through the whole lithosphere which in the fissure swarm is only 4-6 km thick. During the rifting episode the general magma level in the fissure swarm rose to near the surface by 1980, but the loading increments appear to have decreased with time from 1975 to 1980.