We investigate the influence of fault dip (35°–60°) and crustal velocity heterogeneity on rupture dynamics and near-fault ground motions from normal- and reverse-faulting. The same initial conditions were used, except for the direction of initial shear stress, in each dynamic rupture calculation. We used two 3D elastic finite-element approaches that employ split nodes for the computations. In homogeneous and weakly heterogeneous half-spaces with faults dipping ≲50°, maximum fault-normal peak velocities occurred on the hanging wall. However, for fault dips ≳50°, maximum fault-normal peak velocities occurred on the footwall. Bilateral and unilateral rupture simulations in weakly heterogeneous media found that reverse-faulting slip velocities (frequency band 1–3.5 Hz) were on average 39% larger than those during normal faulting. However, on average reverse-faulting slip velocities were only 16% larger than normal-faulting slip velocities for frequencies <1 Hz. This suggests that normal-faulting ground motions may have peak spectral accelerations at distinctly lower frequencies than reverse-faulting ground motions. Normal faults often juxtapose a low-velocity hanging-wall sedimentary basin against relatively stiff footwall rocks. A 3D velocity model was constructed with a thick (several kilometers) low-velocity basin with a strong shear-wave velocity contrast (factor of 3) across a fault dipping 55°. While the strong lateral velocity contrast reduced normal-faulting fault-normal peak velocities on the footwall, substantial (0.5–1 m/sec) fault-normal peak velocities remained on the footwall. Meanwhile even larger fault-normal peak velocities occurred on the more compliant hanging wall. These results indicate that simple amplitude parameterizations based on the hanging wall and/or footwall and the fault normal and/or fault parallel currently used in ground motion prediction relations may not be appropriate for some faults with dips >50°.