The region around the detonation is divided into three zones: (1) a strong-shock (hydrodynamic) zone, (2) a transitional, nonlinear zone, and (3) the elastic region. Experimental equation-of state data are used in calculating the history of the propagating stress wave, because there is as yet no complete theory of the response of solids to rapidly applied stresses which exceed their yield and crushing strength. Results indicate that the proper equations of motion are known, as are analytic and numerical methods for solving them. The theory of shock waves in a fluid is applicable to the close-in region, and several failure mechanisms have been postulated for the transition region. The objective of the analysis is the determination of the stress waveform at the inner boundary of elastic behavior. The peak amplitude and spectral content depend on the yield, the type of medium, and 0ambient stress (depth of burial). The experimental determina tion of the shortest range at which elastic be havior begins is difficult in principle, because solutions valid at great distances are not applicable. (Author)