Digital recordings of ground motion during tremor episodes accompanying eruptions at Mount St. Helens Volcano in the state of Washington on August 7 and October 16--18, 1980, are studied. The spectra of the vertical component waveforms contain at least two dominant peaks at 1.0 and 1.3 Hz for all events recorded during both eruptions that were studied. Spectra of horizontal ground motion show peaks at 0.9 and 1.1 Hz. The relative amplitude of the two peaks changes between tremor episodes and during single tremor episodes and shows no consistent relation to amplitude of ground motion. Spectra of long-period earthquakes are very similar to those of tremor events, suggesting that tremor is composed of many long-period earthquakes that occur over a period of time. The unique waveform of tremor events observed at Mount St. Helens must be due to a source effect, since the relative amplitude of the two dominant peaks changes during tremor episodes. The path effect on tremor waveforms is small since there are no peaks in the spectra of waveforms recorded during tectonic earthquakes occurring in the vicinity of Mount St. Helens. The consistency of the location of the spectral peaks for the wide range of tremor amplitudes means that there must be a physical length at the source that is constant, independent of the amplitude of motion at the source. Variations in amplitude of motion generated during tremor events must be due to variations in the force driving the tremor. Amplitudes of ground motion varies between 0.11 and 4.7 μm. Seismic moment rates during the two eruptions are calculated using the model of Aki et al. (1977) and found to vary between 6¿1018 and 1¿1020 dynes cm s-1, which are larger than values found by Aki et al. (1977), who studied amplitudes of shallow tremor events recorded during the October 1963 eruption of Kilauea volcano in Hawaii. Study of tremor amplitudes recorded at Corvallis. Oregon, leads to the conclusion that tremor accompanying the cataclysmic May 18, 1980, eruption was at least one order of magnitude larger in amplitude than tremor during August and October.