This work is concerned with the formulation of the Total Potential Energy Functional for a Thin -walled Box Column. Specifically, the formulated Energy functional supports the use of Raleigh - Ritz Method – RRM (with polynomial shape functions) in the stability analysis of thin-walled box (closed) columns. The formulated energy functional took its derivative origin from the basic elasticity theories, by the consideration of Equilibrium Equations, Stress- Strain relations, Strain- Displacement relation and work done by external load of an axially compressed single cell thin- walled box column, which was used as case study. The resulted formulation was then transformed in such a way that the
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