Horizontally layered velocity models were used with point‐source and finite‐fault sources to investigate geometrical spreading and the relative amplitudes of vertical and horizontal ground acceleration within 120 km of the source. Full‐wave‐field simulations were done for a range of focal depths and for strike‐slip and reverse focal mechanisms. The attenuation of the geometric mean of randomly oriented horizontal‐component maximum acceleration amplitudes, averaged over all azimuths, significantly exceeds the theoretical geometrical spreading for far‐field body waves in a homogeneous whole space for hypocentral distances less than approximately 60 km. The behavior of the vertical component is different from the horizontal: vertical attenuation near the epicenter is greater and is more dependent on source mechanism and depth. Because of the rapid near‐source decay of the direct S wave, reflections from the mid‐lower crust and Moho control the maximum amplitude of the vertical‐component acceleration in the 60–120‐km hypocenter distance range, resulting in a flattening of the vertical amplitude‐distance relation. Near‐source vertical maximum amplitudes averaged over all source–receiver azimuths tend to be less than the geometric mean horizontal amplitude for strike‐slip focal mechanisms, but, near the source for reverse faults, the azimuthally averaged vertical‐component amplitude exceeds that of the geometric mean horizontal. The modeling indicates that similar vertical‐ and horizontal‐component geometrical spreading and approximately constant horizontal/vertical amplitude ratios observed in connection with the Lg phase at distances greater than approximately 100 km in eastern North America may not hold at smaller distances. Ground‐motion prediction models for the vertical component near the source may need to incorporate strong geometrical spreading and dependence on radiation pattern.