Abstract Complex fault systems are often located in regions with asymmetric topography on one side of a fault, and these systems are very common in Southern California. Along these fault systems, geometrical complexities such as stepovers can impact fault rupture. Previous rupture dynamic studies have investigated the effect of stepover widths on throughgoing rupture, but these studies didn't examine the influence of topography on the rupture behavior. To investigate the effect of asymmetric topography on rupture dynamics at stepovers, I consider three cases: (a) a flat topography, (b) a positive (mountain), and (c) a negative (basin) topography on only one side of the fault system outside of the stepover. In each case, I use the 3D finite element method to compute the rupture dynamics of these fault systems. The results show a significant time dependent variation of the normal stress for the topography cases as opposed to the flat surface case, which can have an important impact on rupture propagation at the stepover. For a positive topography on the right of the rupture propagation, there is a clamping effect behind the rupture front that prevents the rupture to jump a wider extensional stepover. The opposite is observed for a negative topography or for a positive topography on the left side of the rupture propagation, where the rupture can jump over a wider compressional stepover. These results suggest that topography should be considered in dynamic studies with geometric complexities such as stepovers, and perhaps bends and branched fault systems.