Currently, the robustness analysis of structure is primarily related to rigid structures, and little has been done to study the robustness of spatial flexible cable-strut tensile structures with larger span, more complex forms, lower redundancy, more sensitivity to unexpected interference such as construction deviations, etc. Based on the \( H_{\infty } \) theory, this paper starts with the fundamental theory and develops analysis method for the robustness of flexible cable-strut tensile structures, and then the relationships between the structural robustness and some design parameters such as initial pre-stress level, load distribution form, structural span, cross-section area, rise-span ratio, etc. are analysed through a case study of a concrete cable-strut tensile structure in China. On this basis, the effects of construction errors such as element-length error and supporting node position error are further analysed. Finally, the importance of each kind of element is analysed by means of conceptual removal of element. The results show that the higher the initial pre-stress level, the larger the element cross-section, the smaller the structural span, the larger the rise-span ratio and the more uniform the load distribution, the stronger the structural robustness. In the limited construction error range, the element-length error and the supporting node position error have little effects on the robustness of the structure. The hoop cables are the more important elements and the elements in inner region of the structure are of comparatively lower importance in the cable dome structure in this study.