A method has been developed which allows computation, in the inelastic region and near the inelastic-elastic boundary, of the Earth motions resulting from an underground nuclear detonation. It utilizes a one-dimensional digital computer code in which the conservation equations are transformed to difference equations in Lagrangian form. Changes of state from gas to liquid to solid are handled by switching to different equations of state as the internal energy drops below the enthalpy of vaporization and fusion, respectively. Within the solid region, inelastic processes such as plastic yielding, crushing, or cracking are handled by changing the stress deviator equations. Throughout the calculation, the time and space dependence of the shock wave parameters as well as the rate of energy deposition and material behaviour behind the shock front is tied to experimentally determined properties of materials including among others the Hugoniot equations of state. Experimental confirmation of this method is most convincing in the region above 10 kbar, where peak radial stresses measured on detonations in granite, dolomite, and salt agree, within 20 %, with predicted values, and those for detonations in tuff and alluvium agree within 30 %. Measured shock position curves from explosions in granite, tuff, and alluvium are in excellent agreement with calculations. In the lower stress region the calculation is more difficult and not quite as successful. However, we now have substantial agreement between calculated and experimental stress history data from detonations in granite, alluvium, tuff, dolomite, and salt. We also have computed the reduced displacement potential both from calculated and measured displacements at 300 m from the Salmon explosion and find agreement to within 25 % in peak values-about the same as the amount of disagreement that exists between different measurements. This result is encouraging since it opens the possibility of calculating seismic amplitudes from essentially first principles. A two-dimensional computer code with capabilities similar to the one-dimensional one mentioned above also has been devised and is about to become operational. When it does, it will be able to handle two-dimensional sources as well as surface wave propagation problems.