The snow load distribution has a significant impact on the stability of single-layer reticulated shells, a conventional type of long-span space structure. This paper attempts to disclose how the snow load distribution influences the stability of two types of single-layer reticulated shells, namely, spherical reticulated shell and cylindrical reticulated shell. Two influencing factors were taken into account: the asymmetry of snow area on the projection surface of the shell, and the non-uniformity of snow thickness along the radial direction of the shell. The nonlinear finite-element program ANSYS was adopted to calculate the bearing capacities of the two shells under different snow load distributions, in the light of the equilibrium path under each distribution, and to identify the most dangerous distribution of snow load for each shell. The results show that: the asymmetry and non-uniformity have obvious impacts on the stability of spherical reticulated shell, and even greater impacts on that of cylindrical reticulated shell; the most dangerous snow load distributions for spherical reticulated shell and cylindrical reticulated shell are the non-uniform distribution across the half span of the two outermost rings, and the non-uniform distribution across the half span in the middle, respectively. The research results provide reference for keeping large public buildings safe under snow load.