Dip-slip faulting may juxtapose different geologic materials with different properties, such that a strong material contrast will naturally tend to form. Both the material contrast across a fault and dip-slip motion on a nonvertical fault lead to normal stress variations during earthquake rupture. This normal stress variation will significantly affect dynamic rupture propagation. To demonstrate this, we model dynamic rupture propagation on two-dimensional (2D), reverse, and normal faults (30°, 45°, and 60° dipping) with 20% material contrasts. For predominantly up-dip rupture propagation, we find that normal stress variations due to the free surface and material contrast can either reinforce or counteract each other depending on the configuration. For reverse faults, we find a larger strength drop for a more compliant hanging wall and a lower strength drop for a more compliant footwall. For normal faults, we find a larger strength drop for a more compliant footwall and a lower strength drop for a more compliant hanging wall. For both reverse and normal faults, ground motion will be more symmetric between the hanging wall and footwall with compliant material on the footwall and more asymmetric if more compliant materials are on the hanging wall. Our results have important implications for the dynamics of crustal and perhaps subduction-zone earthquake faulting, where strong bimaterial contrasts across dipping faults are possible. In continental settings, reverse faulting will tend to advect rigid materials from greater depth onto the hanging wall, such that the effects of fault dip and material contrast will counteract one another. In subduction zones, the hanging wall is likely to be more compliant, and hence the material and geometric effects may reinforce one another.