The South Iceland Seismic Zone appears to act as a transform fault between offset sections of the Mid-Atlantic Ridge. However, there is no morphological expression of a throughgoing transform between the ridges. The anticipated throughgoing east-west transform is represented by a series of north-south strike-slip faults. We study the mechanics of the South Iceland Seismic Zone using boundary element methods. First, we examine the implications of the differences between the geometry of an orthogonal ridge-transform-ridge system and the geometry of the structures observed in Iceland. Then we consider the role of the north-south faults in accommodating transform motion in an east-west direction. We conclude that the north-south faults can accommodate deformation if they are longer or more spatially frequent than mapped. The South Iceland Seismic Zone is subject to sequences of large earthquakes every 45--112 years. In comparing the seismic moment release derived from eathquake magnitudes with that predicted by our models, we confirm that the system of north-south faults can act as a transform fault. The seismic moment release derived from the earthquake magnitudes is 1.4 times greater than that predicted by our models. If our application of the moment-magnitude relation is correct, the above could imply that the brittle layer extends to 14 km (rather than the 10 km assumed in our models). Other possibilities are that the magnitudes of the earthquakes have been slightly overestimated or that the historical seismic record documents a period of seismicity greater than that expected from rates of the plate motion inferred from geological and Very Long Baseline Interferometry (VLBI). ¿1990 American Geophysical Union