Strike-slip faults can be nonplanar in both their strike and dip dimensions. While a large body of work has investigated the effects of changes in strike on earthquake rupture and arrest, no previous studies have investigated the role of along-strike variations in dip on strike-slip ruptures. Here, I use the three-dimensional finite-element method to conduct dynamic simulations of ruptures on strike-slip faults with linear surface traces and changes in dip along strike. I experiment with the amount of dip change as well as the abruptness of that change under a variety of initial stress conditions. In all of my initial stress cases, I find that a change in dip along strike can cause rupture to stop, and that larger dip changes over shorter distances are more likely to do so. This is largely due to the change in strike at depth that inherently comes from changing the dip; the majority of these behaviors are a result of the rupture front being forced to change direction mid-rupture. While some dip-slip movement does occur on the nonvertical parts of the model fault, it does not have a significant effect on rupture extent. However, linear-surface-trace, nonvertical-dip faults do produce different surface slip, stress, and ground motion patterns compared to corresponding nonlinear-strike, vertical-dip faults. Together, my results show that changes in dip along strike-slip faults do considerably impact the rupture process, suggesting that this type of geometrical complexity should be considered in rupture forecasts and hazard assessments.