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For a long time, spatial structures have been widely used. However, compared with the high strength of their material, their stability is weak, and especially sensitive to damage and defects. This feature has increased the engineering industry’s high requirements for their stability analysis. As we all know, this problem is more prominent for the reticulated shell structure, which is a classic representative of the spatial structure. However, in the current analysis methods for the stability of reticulated shells, the deterministic analysis method cannot consider the random characteristics of defects. Other random methods, such as the random defect modal method, and many improved methods, require more samples and calculation time. This unfavorable situation makes its engineering application greatly restricted. In addition, the random modal superposition method and derivation method based on Monte Carlo has not fundamentally changed this limitation. In order to fundamentally overcome this traditional shortcoming, this paper comprehensively studies the advantages of the high accuracy of the random defect modal method and the improved method, and at the same time, investigates the speed advantage of the response surface method, and then creates a new stochastic analysis method based on the response surface method. Finally, the analysis results of the calculation examples in this paper prove that it successfully balances and satisfies the dual requirements of accuracy and speed required for calculating the stability of the reticulated shell structure. Moreover, it has universal applicability to different forms of reticulated shells, such as classic 6-point flat domes, traditional reticulated shell structures, and bionic reticulated shell structures, and even other types of spatial structures.