The stochastic model used previously to estimate motions at hard-rock sites in eastern North America has been modified to include the effect of deep soils. We simulated motions for a number of distances and magnitudes for a representative soil column and used these motions to derive equations giving ground motion as a simple function of magnitude and distance. These new equations are intended for use in building codes and those engineering applications that do not require detailed site evaluations. The ground motions for which we derived equations include 5%-damped response spectra at 13 periods ranging from 0.05 to 4 sec, peak acceleration and the maximum pseudovelocity and maximum pseudoacceleration responses. The latter two quantities are introduced here for the first time. They represent the maxima over the period range 0.1 to 4 sec for a given magnitude and distance, and they may be useful as a basis for determining the seismic coefficient in building codes.