Abstract: Solar greenhouses have been widely used in the vast western and northern regions of China, due mainly to the convenient construction and installation, low economic cost, and outstanding environmental adaptability. The slender steel can be the load-bearing components of the section-steel arched solar greenhouse to resist external loads, such as wind and snow. There are the prominent instability and disaster that caused by insufficient stiffness of solar greenhouse under extreme weather conditions, such as snowstorms. In this study, the nonlinear stability analysis was conducted on the commonly-used section-steel arched solar greenhouse in Hebei using elastic-plastic mechanics and nonlinear finite element (FE). A refined FE model was established for the section-steel arched solar greenhouse. The greenhouse arch roof and the vertical sections on both sides were simulated using the Beam188 element in the element library of the universal FE analysis program ANSYS. The linear elements were used to fit the circular arc segments. Diagonal tension bars, vertical brace struts, and longitudinal tie bars were all simulated using Link10 element. The bottom of the vertical sections on both sides of the arch was assumed to be consolidated with the foundation. The steel was made of Q235, with an elastic modulus of 206 GPa, a Poisson's ratio of 0.3, and a density of 7 850 kg/m³. Geometric and material nonlinearity was considered to simulate the constitutive relationship of steel using an ideal elastic-plastic model, followed by von Mises yield criterion and bilinear kinematic hardening model BKIN. The stability performance and parameter analysis of solar greenhouse structure were carried out under snow loads. The stability capacity of solar greenhouse was determined under different parameters, such as steel-section type (flat elliptical, hollow rectangular and hat-shaped cross-section), greenhouse span (8, 10, and 12 m), and snow load distribution pattern (non-uniform distribution thickness and asymmetric distribution area). There was the quantitative influence of snow load distribution on the stability capacity of solar greenhouses. The load factor-displacement curves were combined with the deformation, stress, axial, and bending moment at different points of loading time. The static instability of solar greenhouses was explored from two aspects: intuitive phenomena and intrinsic essence. The conclusions were obtained as follows: The stability capacity of the steel component with a flat elliptical section in the solar greenhouse was increased by 21.0% and 44.2%, respectively, compared with the box and hat-shaped section. There was no out of plane instability in the same cross-sectional area and flange width of the steel component. The stability capacity of solar greenhouse was rapidly reduced with the increase of span. The stability capacity of solar greenhouse under non-uniform distribution of snow loads was reduced by the maximum of 63.8%, compared with the uniform. The maximum stability capacity of a solar greenhouse increased by 9.0% and 66.8% with only tension bars and brace struts, respectively. The findings can provide the technical guidance and theoretical reference for the anti-snow loads, stability and disaster prevention in the section-steel arch solar greenhouses.