Vessels used to contain the effects of high explosions are designed in a wide variety of shapes, sizes and materials. L's Alam's National Laboratory has used spherical pressure vessels to conduct high-explosive detonation experiments for over 30 years. The militarys explosives ordnance demolition (EOD) community uses pressure vessels to destroy aged conventional and chemical munitions. Issues associated with the differences between transient and static pressures and their influences on the structural response of these vessels are addressed in this report. These issues are illustrated by reference to an example spherical containment vessel for containing high explosives (HE), but the concepts are generally applicable to containment vessels of any shape or construction. In the past, design of these containment vessels was typically accomplished by maintaining that the vessels kinetic energy, developed from the detonation impulse loading, be equilibrated by the elastic strain energy inherent in the vessel. Within the last decade, designs have been accomplished utilizing sophisticated and advanced computer codes that address both the detonation hydrodynamics and the vessels highly nonlinear structural responses. Notwithstanding the past accomplishments, no industry design standard(s) or guidelines have ever been developed to address a complete and rational design philosophy for detonation impulse loading of a pressure vessel. Nevertheless, this document provides the basis for the nonlinear dynamic loading associated with HE detonations, the resulting nonlinear and highly complex vessel response, and the static loading associated with the residual quasi-static overpressure. Understanding the dynamic events under detonation conditions is the first step towards the development of rational pressure vessel design criteria. Ultimately, it is hoped that the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code will adopt a vessel design standard for HE detonations.