Safety against buckling under wind loading is an important criterion in the design of cooling tower shells. A rigorous bifurcation analysis of a cooling tower shell subjected to actual non-axisymmetric wind pressure distribution using quadrilateral or triangular elements is time consuming. An attempt at such an analysis using ring elements in the form of a frustum of a cone with only four degrees of freedom per nodal line has yielded encouraging results. The coupling of harmonics that occurs in a bifurcation analysis using a Fourier series has been found to be only of minor disadvantage in the computational efforts. A computer program has been developed using this alternative method. No simplifying assumptions such as equivalent axisymmetric pressure or stress have been made for wind pressure effects. The results obtained from the present analysis are compared with the results available in the literature. © 1991.