This thesis is concerned with near source primary seismic waves generated by, the Gnome, Hardhat, Shoal and Haymaker underground nuclear explosions. Records of ground motion between 0.3 and 20.0 kilometers from the sources were analyzed in terms of displacement amplitude and energy variations with distance. The observed data have been compared to similar data from a theoretical source model to determine the adequacy of the theoretical model. The Fourier Integral has been used to obtain frequency analyses of the first half cycle of the primary displacement waves in the near source region to the observed and theoretical sources. There is some evidence that a long period displacement field may exist near the explosions, as predicted by the theoretical source. Scatter in the observed amplitude data makes it difficult to distinguish between the long period and the radiation fields. The variation with distance of total energy of the primary seismic waves indicates that the radiation field becomes representative of the energy beyond a few kilometers from the sources. When the conditions are approximated, for which the theoretical source was developed, the comparison of observed and theoretical data indicate that the theoretical source approximates the observed sources. It was found that the waveforms from the theoretical source did not approximate the waveforms from the Haymaker explosion and from one quadrant of the Shoal explosion. This is thought to be due to any combination of the following reasons: (a) the elastic-inelastic boundaries were not correctly defined for these observed sources, (b) the media were not elastic and elastic theory did not apply, and (c) the solution for the theoretical displacement pulses given by the theoretical model does not apply to all cases.