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Abstract: The disassembly theory of reactor safety analysis developed for early metal-fueled criticals is applied to determining the potential nuclear explosive yield of reactor-grade plutonium. After verification of the theoretical models, materials data, and equation of state by recalculation of published data, this disassembly theory is applied to so-called hypothetical nuclear explosive devices (HNEDs) based on reactor-grade plutonium. The masses for k eff =0.98 and the neutron life times are calculated for such devices by applying neutron transport theory and Monte Carlo codes. Spherical shock compression models describe the density variations as a function of space and time for spherical shock compression of the reactor-grade plutonium sphere with a natural-uranium reflector. Reactivity calculations are performed to determine “Rossi alpha” as a function of time during spherical shock compression. Pre-ignition theory shows that pre-ignition by spontaneous fission neutrons occurs just after prompt criticality is achieved. The chain reaction and power excursion initiated lead to internal pressure buildup which stops the spherical shock wave after it has penetrated between 1.3cm and 1.8cm into the plutonium metal sphere. This limits the maximum reactivity input and the potential nuclear explosive yield to 0.12 up to 0.35kt TNT (equivalent). However, these results do not describe the full reality. In a companion paper, thermal analysis shows such HNEDs to be technically unfeasible for all reactor-grade plutonium from spent LWR fuel with a burn-up of more than 30GWd/t as long as low technology is used in the spherical implosion lenses of chemical high explosives. More advanced medium technology would raise this burn-up limit to approximately 55GWd/t. [Copyright &y& Elsevier]