A random-vibration model of the Hanks-McGuire type is used to predict peak ground motions at rock sites in eastern North America. The assumed geometric decay and distance-dependent duration approximate the propagation of direct body waves (at short distances) and Lg waves (at regional distances). The model predicts peak acceleration and velocities, as well as response spectra and magnitude for a given seismic moment and corner frequency. To predict ground motions for a given Lg magnitude (mLg), the model is first used to calculate the seismic moment corresponding to that magnitude, assuming a source scaling law. Then, knowing the moment and corner frequency, the model is used to calculate peak ground motions. Available data from strong motion recordings and from the ECTN and LRSM networks, modified to estimate horizontal ground motions on rock where appropriate, are used to verify the model's assumption and predictions. Modified Mercalli intensity data are also used. Ground motions predicted by the model with a stress drop of 50 to 200 bars agree with the ground motion data, but the mLg values computed by the model for given seismic moments do not agree with Nuttli's (1983) moment versus mLg data for large earthquakes. Resolution of the latter disagreement awaits the collection of instrumental data from large events in eastern North America.