A systematic presentation of methods for analyzing both steady and transient stress loadings on diverse objects under various circumstances, and specific numerical findings for dynamic stress concentrations on objects of different shapes. The report shows clearly that the scattering of elastic (stress) waves is no different from the scattering of sound or electromagnetic waves, and much of the analysis is based on wave propagation methods. Ironically, the elastic solid theory used was originally developed to explain the diffraction of light — and was abandoned after the electromagnetic wave and quantum theories of light appeared. When Rand began studying survivability of hardened military systems in 1960, there were few solutions and few numerical results for dynamic stress concentration factors. A decade later, there were many; this volume summarizes an extensive literature. Results are widely applicable in, for example, machine design and structures analysis, composite materials, analysis of flaws in materials, and earthquake resistance.