The perturbation method is applied in an incremental scheme for tracing non-linear equilibrium paths of structures which are subjected to a set of simultaneously acting external loads. The method is based on the discretesized version of the non-linear stability theory and it is used for solving non-linear algebraic equations. In order to pass limit points, the direct arc length concept is introduced. The method is especially adapted to the solution of plate buckling problems for which both strength and in-plane stiffness properties are important parameters. As an example, the perturbation procedure is used for solving a simple plate buckling problem, for which a closed form solution exist, and the results were compared to results from a recognised non-linear finite element program.