The treatment of wastes on a nuclear level and transforming them into safer isotopes by selectively irradiating the wastes with a variety of particles including neutrons, protons, and beta and alpha particles is investigated. The goal is to significantly reduce the number of certain isotopes that present the most severe biological hazards. Among these are cesium and iodine which, when collected, remain in the human body and the transuranic elements are not only radioactive but highly toxic. The investigation involves mathematical modeling of the transmutation of isotopes under irradiation. The model includes all isotopes found in high level waste under all forms of irradiation. The process is repeated for all possible resulting products through any series of transmutation. A computer code is to be developed to solve simultaneously all of the coupled levels of the irradiating particles and the duration of the irradiation. The code is utilized to achieve a series of irradiations by the various particles at feasible flux levels yielding the desired result.