The back-structure is an important part of the supporting system of the FAST reflectance surface.Its performance directly affects the precision of the FAST and its costs.In this paper,a shape-keeping method for the design of sub-structures is proposed.Then several kinds of back-structures are provided,followed by optimization of the advanced back-structures such as spatial latticed,strain stressed and hybrid structures.After a comparison of their structural behaviours and manufacturing processes,it is concluded that the double-layer latticed structure in local areas has advantages of small weight,large stiffness and easy manufacturing process.