Factors that control the rupture processes across the 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 rupture processes beyond fault discontinuities are drastically different between the two models. W 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. Whether rupture on the first fault reaches the surface or not, especially, controls the difficulty and locations of rupture jumps. This is because the stress perturbation is affected by the free surface.