GPS geodetic observations 1986--1992 spanning the oblique plate boundary on the Reykjanes Peninsula, SW Iceland, show that left-lateral shear strain is accumulating in the area. The principal strain rates are &egr;˙1=0.255¿0.055 &mgr;strain/yr (extension) at N121¿6¿E, and &egr;˙2=-0.190¿0.053 &mgr;strain/yr (contraction) at N31¿6¿E. The principal axis of extension is perpendicular to the strike of fractures within volcanic systems on the Peninsula. The direction of maximum left-lateral shear strain is N76¿6¿E, the same as the trend of the seismic zone on the Peninsula. Tensor shear strain in this direction is -0.222¿0.054 &mgr;strain/yr. Continuous aseismic slip of the North American-Eurasian plates below a 5--11 km locking depth on the Peninsula can explain the observed depth of earthquakes, the width of the deformation zone determined from recent fissuring and faulting, and the GPS-measurements of strain. ¿ American Geophysical Union 1994