Journal of Nuclear Materials Vol.441 Nr.1-3, 473 - 486 ; In this work, the Monte Carlo burn-up code SERPENT-2 has been extended and employed to study the material isotopic evolution of the Molten Salt Fast Reactor (MSFR). This promising GEN-IV nuclear reactor concept features peculiar characteristics such as the on-line fuel reprocessing, which prevents the use of commonly available burn-up codes. Besides, the presence of circulating nuclear fuel and radioactive streams from the core to the reprocessing plant requires a precise knowledge of the fuel isotopic composition during the plant operation. The developed extension of SERPENT-2 directly takes into account the effects of on-line fuel reprocessing on burn-up calculations and features a reactivity control algorithm. It is here assessed against a dedicated version of the deterministic ERANOS-based EQL3D procedure (PSI-Switzerland) and adopted to analyze the MSFR fuel salt isotopic evolution. Particular attention is devoted to study the effects of reprocessing time constants and efficiencies on the conversion ratio and the molar concentration of elements relevant for solubility issues (e.g., trivalent actinides and lanthanides). Quantities of interest for fuel handling and safety issues are investigated, including decay heat and activities of hazardous isotopes (neutron and high energy gamma emitters) in the core and in the reprocessing stream. The radiotoxicity generation is also analyzed for the MSFR nominal conditions. The production of helium and the depletion in tungsten content due to nuclear reactions are calculated for the nickel-based alloy selected as reactor structural material of the MSFR. These preliminary evaluations can be helpful in studying the radiation damage of both the primary salt container and the axial reflectors.