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In this paper, the static stability of the variable cross section columns, subjected to distributed axial force, is considered. The presented solution is based on the singular perturbation method of Wentzel-Kramers-Brillouin and the column is modeled using Euler-Bernoulli beam theory. Closed-form solutions are obtained for calculation of buckling loads and the corresponding mode shapes. The obtained results are compared with the results in the literature to verify the present approach. Using numerous examples, it is shown that the represented solution has a very good convergence and accuracy for determination of the instability condition