Radiopharmaceuticals are used in nuclear medicine for diagnostic or therapeutic acts. The short decay half-lives of medical radioisotopes, especially those used for diagnostics, imply that they should be produced continuously and transported as quickly as possible to the medical units where they are used. Neutron-rich medical radioisotopes are generally produced in research reactors, like technetium-99m, lutetium-177, holmium-166 and iodine-131. On the other hand, proton-rich radioisotopes are produced via reactions with charged particles from accelerators like fluorine-18, gallium-67, iodine-123 and thallium-201. Beside this, innovative nuclear reactors are advocated as solutions to the issues of nuclear waste production and proliferation threats. Fast neutron, thorium-cycle and accelerator-driven subcritical (ADS) reactors are some of the most promising of them, proposed as safer fuel breeders and “waste burners”. This article examines the use of a fast thorium-cycle ADS with liquid lead-bismuth eutectic coolant for the production of molybdenum-99/technetium-99m and lutetium-177. Burnup simulation has been made with the Monte-Carlo (MC) code SERPENT. It is demonstrated that MC codes can advantageously be used to determine the optimal irradiation time for a given radioisotope in a realistic reactor core. It is also shown that fast thorium-cycle ADS is an economical option for the production of medical radioisotopes.