The aim of this study is to analyze the transmutation of Long Lived Fission Products (LLFPs) using an accelerator based system. The seven LLFP's are investigated based upon their decay mechanics, yields from fission, and neutron absorption cross sections to select potential target nuclides. MCNPX is the primary modeling tool used. Infinite targets are modeled to determine dependence on the energy of the incident beam. Finite targets containing only nuclides to be transmuted are modeled to compare different LLFPs and finalize the target nuclide selection of 99Tc. Custom cross sections are produced in MCNPX in order to model a target containing other materials and multiple regions. A cylindrical target design is decided upon where the 99Tc content and the dimensions of the target are varied to improve transmutation characteristics. The final target design contains 131 kg of 99Tc mixed with lead in a cylindrical target with a radius of 40 cm and a length of 120 cm, with a cylindrical hole with a 10 cm radius extending 30 cm into the technetium-lead region and a cylindrical graphite reflector region extending 40 cm radially from the target, 50 cm from the front of the target and 80cm from the back of the target. The incident particle energy requirement per transmutation is 56.9 MeV. Using a 1200 MeV proton beam with a power of 2.4 MW (the rate at which the kinetic energy of protons enters the target), the transmutation rate obtained under continuous operation is 1.36 kg/year, corresponding to an initial effective halflife of 66.7 years.