A single-layer cylindrical reticulated shell was taken as an example to study the influence of snow-drifing on the dynamic stability of spatial structures under coupled wind and snow loads by the Budiansky-Roth criterion. Stochastic wind loads on the structure were obtained from the wind tunnel test, and the snow-drifting on the structure under wind actions was simulated by the numerical method based on FLUENT with added C++ code. The results show that snow erodes on the top of the shell while deposits on the windward and lee side of the shell. The angle of the dividing line between the erosion area and the deposition area is identical to the corresponding wind direction. The snow-drifting on the shell debases its dynamic stability in all typical wind directions. The longer the duration of snow-drifting the worse the dynamic stability of the shell, but the influence of snow-drifting decreases with its duration. Also, the dynamic stability of the shell recedes with the increment of original snow depth on the shell.