Folded plates have attracted profound interest in recent years because of their economic advantages and architectural appearance. In particular, their basic structural response is indeed logical enough, explicit and simple although its required numerical computation procedure is, in a little bit, boring. This type of structures have gained increasing popularity and offers more advantages than more complex structures, such as cylindrical shells, arches and right folded plate frames. Similarly, the thin-walled cellular bridge decks can be treated as a multi-folded plates structure. This study produces an overall review of the historical development of the most popular methods utilized for analysis the folded plate structures which are offered with their applications and how these methods are developed gradually. Four common methods are chosen in this paper to show their highlights of references particularizing in analysis of the above mentioned types of structure; the folded plate elasticity method (FPEM), finite element method (FEM), finite strip method (FSM) and spline finite strip method (SFSM). This investigation covers the elastic behavior, and the experimental researches on the elastic reaction of folded plate structures.