This master’s thesis deals with usage of burn-up (spent) nuclear fuel in nuclear power plants of next generation – accelerator driven transmutation plants which is produced in current nuclear power plants. This system could significantly reduce the volume of dangerous long-lived radioisotopes and moreover they would be able to take advantage of its great energy potential due to fast neutron spectrum. In the introduction are listed basic knowledge and aspects of spent nuclear fuel along with its reprocessing and the possibility of further use while minimizing environmental impact. As another point detailed description of accelerator driven systems is described together with its basic components. In addition this search is followed by individual chronological enumeration of projects of global significance concerning their current development. Emphasis is placed on SAD and MYRRHA projects, which are used like base for calculations. This last, computational part, deals with the creation of the geometry of subcritical transmutation reactor driven by accelerator and subsequent evaluation which assembly is the most effective for transmutation and energy purposes along with changing of target, nuclear fuel and coolant/moderator.