Static stress change has been proposed as a mechanism of earthquake triggering. We quantitatively evaluate this model for the apparent triggering of aftershocks by the 1992 MW 7.3 Landers and 1994 MW 6.7 Northridge earthquakes. Specifically, we test whether the fraction of aftershocks consistent with static stress change triggering is greater than the fraction of random events which would appear consistent by chance. Although static stress changes appear useful in explaining the triggering of some aftershocks, the model's capability to explain aftershock occurrence varies significantly between sequences. The model works well for Landers aftershocks. Approximately 85% of events between 5 and 75 km distance from the mainshock fault plane are consistent with static stress change triggering, compared to ~50% of random events. The minimum distance is probably controlled by limitations of the modeling, while the maximum distance may be because static stress changes of <0.01 MPa trigger too few events to be detected. The static stress change triggering model, however, can not explain the first month of the Northridge aftershock sequence significantly better than it explains a set of random events. The difference between the Landers and Northridge sequences may result from differences in fault strength, with static stress changes being a more significant fraction of the failure stress of weak Landers-area faults. Tectonic regime, regional stress levels, and fault strength may need to be incorporated into the static stress change triggering model before it can be used reliably for seismic hazard assessment. ¿ 1998 American Geophysical Union