We simulated spontaneous dynamic rupture propagation on a branched fault system using the boundary integral equation method (BIEM) in 3D homogeneous, unbounded elastic medium. From the numerical experiments, we found that slightly heterogeneous preload stress field on the branches caused selective rupture propagation. Dynamic rupture propagation spontaneously on both branches requires very delicate conditions for the initial stress field as well as for the fracture criterion on them. ¿ 2000 American Geophysical Union