This study assesses the feasibility of designing a Molten Salt Reactor (MSR) using the salt mixture of LiF (15 mol%), NaF (58 mol%) and BeF 2 (27 mol%) to be critical when fuelled with TRU from LWR spent fuel without exceeding the actinides solubility limit and while extracting fission products at realistic rates. The first part of the study investigated the graphite-to-MS volume ratio on the neutron balance, transmutation characteristics and graphite lifetime. It is found that a core without graphite moderator is the preferred design option; it offers the best neutron balance, most compact design and alleviated graphite lifetime problem. The second part of the study investigated sensitivity of the epithermal spectrum core to the feed composition, power density, fission products residence time and actinides loss fraction. It is found that the transmutation effectiveness improves with increasing power density and that the shorter the LWR spent fuel cooling time is, the better becomes the MSR neutron balance. The optimal MSR design offers a remarkably high transmutation capability e fissioning of as high as 99.8% of the TRU fed. The transmutation capability of the MSR is also rated in terms of final waste radiotoxicity, decay heat, spontaneous fission neutrons emission, fissile and 237 Np inventory.