The near-field motion on the surface of a uniform half-space for oblique-slip and dip-slip faults has been studied by the use of a dislocation model. The fault is modeled by an infinitely long buried dislocation of finite width; rupture propagates horizontally along the fault and past the observation points with a constant rupture velocity lower than the Rayleigh wave velocity. In addition to those parameters which control peak amplitudes near a vertical, strike-slip fault (depth of the top of the fault, horizontal rupture velocity), the dip of the fault plays an important role. The slip direction and the angle between the rupture front and the down-dip direction of the fault also become increasingly important in determining amplitudes of peak ground motions as the dip of the fault decreases from vertical to shallow angles. In some regions near a thrust fault, peak amplitudes are significantly greater than the largest values near a vertical, strike-slip fault.