Earthquake rupture sometimes occurs on several faults, and often decelerates or terminates at fault stepovers. Factors that control the rupture processes across stepovers are important to an understanding of earthquake growth and termination. In this study, we investigate such factors by calculating the spontaneous rupture processes of two non-coplanar faults in a three-dimensional model. Dealing with two extreme models in which two strike-slip faults are either parallel or perpendicular, we show that the rupture processes beyond fault discontinuities are drastically different between the two models. We find three factors influencing rupture processes beyond fault discontinuities: depth of the upper edge of the two faults, location of the edge of the first fault, and geometry of the two faults. These factors determine the time and location of rupture jumps to the second fault. For rupture propagation to the second fault, it is essential for rupture on the first fault to arrive at the edge of the fault. Whether rupture on the first fault reaches the Earth's surface or not, especially, controls the difficulty of rupture jumps and the locations where the rupture is triggered, which is also related to the step direction of the two faults. This is because the stress perturbation at the fault edge is affected by the free Earth's surface.