A 3-D finite difference method is applied in this study to investigate a spontaneous rupture within a fault system which includes a primary thrust fault and two strike-slip sub-faults. With the occurrence of a rupture on a fault, the rupture condition follows Coulomb's friction law wherein the stress-slip obeys the slip-weakening fracture criteria. To overcome the geometrical complexity of such a system, a finite difference method is encoded in two different coordinate systems; then, the calculated displacements are connected between the two systems using a 2-D interpolation technique. The rupture is initiated at the center of the main fault under the compression of regional tectonic stresses and then propagates to the boundaries whereby the main fault rupture triggers two strike-slip sub-faults. Simulation results suggest that the triggering of two sub-faults is attributed to two primary factors, regional tectonic stresses and the relative distances between the two sub-faults and the main fault.