The South Iceland Seismic Zone (SISZ) accommodates E‐W translation due to oblique spreading between the North American and the Eurasian plates in South Iceland with ruptures on N‐S faults. Strain is released in earthquake sequences that last days to years, at average intervals of 80–100 years. Two M6.5 earthquakes struck in the SISZ in June 2000, and two M6 earthquakes in May 2008. These events released only half of the strain accumulated since the last earthquake sequence in 1896–1912. GPS station velocities are estimated from annual campaigns and continuous measurements in the SISZ during 2001–2015. The GPS station velocities are used to calculate strain rates from a new method using the vertical derivatives of horizontal stress. Our new strain rates are obtained by integrating vertical derivatives of horizontal stress rates, rather than differentiating interpolated GPS velocities, allowing finer resolution of strain. Estimating the strain rates for eight time intervals, we find high strain rates in the SISZ (0.5–1 microstrain per year) with significant temporal and spatial variation. The strain rates in the SISZ reveal contraction in the Hengill area and dilatation over a large area in eastern SISZ, indicating inflation of the magma system beneath Hekla volcano. A prominent strain anomaly is evident in the epicentral area prior to the May 2008 earthquakes. We suggest that this signal is primarily caused by plate motion and an increase in the rate of contraction in the Hengill area, located ∼10 km west of the epicentral area.