Investigations of historic surface‐rupturing thrust earthquakes suggest that rupture can jump from one fault to another up to 8 km away. Additionally, there are observations of jumping rupture between thrust faults apart. In contrast, previous modeling studies of thrust faults find a maximum jumping rupture distance of merely 0.2 km. Here, we present a dynamic rupture modeling parameter study that attempts to reconcile these differences and determines geometric and stress conditions that promote jumping rupture. We use the 3D finite‐element method to model rupture on pairs of thrust faults with parallel surface traces and opposite dip orientations. We vary stress drop and fault strength ratio to determine conditions that produce jumping rupture at different dip angles and different minimum distance between faults. We find that geometry plays an essential role in determining whether or not rupture will jump to a neighboring thrust fault. Rupture is more likely to jump between faults dipping toward one another at steeper angles, and the behavior tapers down to no rupture jump in shallow dip cases. Our variations of stress parameters emphasize these toward‐orientation results. Rupture jump in faults dipping away from one another is complicated by variations of stress conditions, but the most prominent consistency is that for mid‐dip angle faults rupture rarely jumps. If initial stress conditions are such that they are already close to failure, the possibility of a long‐distance jump increases. Our models call attention to specific geometric and stress conditions where the dynamic rupture front is the most important to potential for jumping rupture. However, our models also highlight the importance of near‐field stress changes due to slip. According to our modeling, the potential for rupture to jump is strongly dependent on both dip angle and orientation of faults.