The structure systems with non-rigid member were classified by the composition type of line and surface members. As a result of the classification, there are 1-way cable structure, cable net and radial cable net structure in the line member system. And there are pneumatic structure and suspension membrane structure in surface member system. In addition, when the line and surface members are composed together, there is the hybrid membrane system which are divided into hanging type and supported type. In this paper, the Korean terms of structure systems with non-rigid member are recommended through this classification. In each the structure systems with non-rigid member, the examples were also investigated considering their historical developments. It present that the light weight structure system and the openness of space have pursued with the developments. So largely, cable net structure with membrane, membrane structure and hybrid structure have used in these days.