The main objective of this paper is to propose a new closed form solution, useful in the pre-design stage, that allows one to calculate the mean load in the case of post-collapse of polygonal thin-walled columns in the axial crushing case. This model gives a rapid and accurate evolution of the normalized mean load as function of the corner element angle as well as the ratio between the corner length and the column thickness. To identify the parameters of this model, numerical simulations with an explicit finite element software have been carried out and then compared to experimental results reported in the literature. Finally, all these results combined with the findings based on the known generalized mixed model developed by other researchers working on this topic enabled one to establish the closed form solution. This is a unified and continuous closed form solution, which is suitable for different columns shapes, even non-conventional shapes obtained thanks to the development of extrusion techniques.