The rotation frame is a key component of the amusement equipment. The natural frequency and buckling strength of the rotation frame have a direct impact on the stability of the structure. Finite element software ANSYS Workbench was used to establish a finite element model of the rotation frame. The natural frequency that had the most significant influence on the rotation frame was obtained through the modal analysis and harmonic response analysis. The buckling eigenvalue when the structure was unstable was obtained through buckling stability analysis. Then 140 test points were obtained by using the experimental design. In order to explore the sensitivity of various design variables to the natural frequency and buckling strength of the rotation frame, a BP(back propagation) neural network mathematical model was established through MATLAB software to fit test points. Combining the use of Isight and MATLAB, a descriptive Monte Carlo sampling method was used to numerically simulate the neural network model. The research results showed that the most dangerous modes that had a significant influence on the stability of rotation frame were the 10th to 12th modes. The result of parameter sensitivity analysis indicated that the parameters which had a mainly affect on the rotation frame dangerous modal frequencies were the limb wall thickness, limb section length and limb section width, in addition, the structure parameters which had the most significant influence on the structural buckling stability were six dimensional parameters of the slewing shank, the web, and the circular plate. The conclusion shows that the reasonable improvement of a part of design parameters that effect on the stability of the rotation frame will effectively improve the structural stability and design efficiency. This will provide a certain reference for the subsequent design improvement and optimization of the structure.