Abstract: Abstract: A single-layer reticulated dome structure is elegant and has reasonable stress distribution and various grid types. It has been widely used in various projects, and its stability problem has become the focus of research work. Single layer two-way grid reticulated domes are superior in aesthetic and material efficiency but have a low rigidity. In recent years, researchers worldwide have conducted a series of studies on the low structural rigidity of a two-way grid dome. In these studies, diagonal cables for the two-way grid are used to strengthen the in-plane rigidity of the structure and to improve the overall stability of the reticulated shell structure; the validity of the cable arrangement method is confirmed via testing and theoretical analysis. But researchers have not proposed arrangement of cables between non-adjacent nodes at the out-of-plane of the reticulated dome to improve the rigidity of out-of-plane of the structure. Therefore, to increase the rigidity of the in-plane and out-of-plane of a single-layer two-way grid reticulated dome, cables are installed in diagonals and at the out-of-plane of the reticulated dome. Hence cable installation pattern is considered to increase the in-plane and out-of-plane rigidity of two-way grid domes with width 30, 40 and 50 m. A new cable-strengthened single-layer reticulated dome system is developed for dome structure design. To further investigate structure stability before and after the cable-strengthened reticulated dome develops instability, in this study, an analysis of the complete non-linearity process was employed to perform large-scale parameterization analysis for a reticulated dome structure under various cable arrangement scenarios. More than 500 examples of reticulated domes were carried out with considering both geometric and material nonlinearity based on commercial finite element software ANSYS and self-compiled pre-post-processing programs. The effects of cables and various structural responses such as critical loads, buckling modes, and plastic development levels were examined by the numerical study. The rise-span ratio, cable pre-stress, initial geometric imperfection and unsymmetrical distribution of loads were collected to investigate the stability of reticulated domes. In the numerical calculations, cable arrangement at interior and exterior surfaces of the two-way grid reticulated dome structure effectively improved the bearing capability of the structure, with an improvement range of 29%-92%. Cable pre-stress was more effective in improving the bearing capability of a large span reticulated dome structure than small span reticulated dome structure. The stability of a cable-strengthened single-layer reticulated dome structure was affected by an asymmetric load distribution and initial geometric imperfection; bearing capacity decreases to various degrees. Through a statistical analysis of elastic and elasto-plastic stability critical loads, a plasticity reduction coefficient for the cable-stiffened single layer two-way grid domes was proposed to reveal the influence of material nonlinearity on critical loads. As a result, the plastic reduced coefficients of cylindrical shells were summarized to be 0.7 - 1.0. The impact of material non-linearity on various types of reticulated dome structures had little influence on the structural stability bearing capacity, and the plastic reduction coefficients were above 0.7 Through the analytical results, the elasto-plastic stability behaviors of cable-stiffened single layer two-way grid domes were concluded, and the results provide a theoretical basis and technical support for the practical engineering in modern greenhouse construction.