Abstract: The five-hundred-meter Aperture Spherical radio Telescope (FAST) hasseveral innovations and key technologies involved in multipleengineering disciplines, where mechanics plays a key role in thedevelopment, construction and maintenance of the telescope. A lotof design concepts about the excavation and support work of theKarst depression, the active reflector and feed support are basedon the relative analyses in mechanics. An overall review in a spanof the last ten years is given on the research progress inmechanics of the FAST feed support, where more attention is paidon the current research difficulties or problems further to becracked. Compared with rigid feed support structure of manytraditional telescopes, the FAST feed support is an innovativelyflexible mechanism, so there are many possible options almost forthe design of every subsystem or mechanical unit, and an optimalone has to be selected from them. As a result, it is also urgentfor the researchers to compare all possible concepts fromviewpoint of mechanics and to provide reasonable analysis on whicha final optimal design might be justified.