Most earthquakes take place on geometrically complex fault systems rather than simple planar faults. Recent earthquakes on such fault systems have shown quite clearly the important effects of fault geometry on the dynamics of earthquake rupture, slip, and ground motion. This project is to study the dynamics of geometrically complex fault systems over multiple earthquake cycles using numerical simulations. Specific fault geometries to be addressed include faults with bends, faults with branches, and faults with offset segments. To accomplish this task, dynamic models for the earthquake rupture and slip process are being integrated with quasi-static models to simulate the processes of slow tectonic loading, nucleation, and post-seismic relaxation. An integrated algorithm to model these processes is being developed in this research. Using this technique, the researchers are modeling the complete earthquake cycle: initial stress distributions on faults before an earthquake rupture are a consequence of slow tectonic loading, stress relaxation, and residual stress from previous ruptures. Nucleation is also be spontaneously developed, and dynamic rupture patterns and ground motion are calculated. Thus, the long-term effects of fault geometry and characteristic behaviors of fault systems over multiple earthquake cycles are addressed in a self-consistent manner. The results will aid in the interpretation of recorded earthquakes on geometrically complex fault systems, such the Hector Mine and Chi-Chi events. The results will also aid in the prediction of future behavior of complex fault systems such as the San Andreas, as well as the ground motion during earthquakes on these faults.