A variational model that describes the nonlinear interaction between the global and local buckling of a thin-walled I-section strut under pure compression is presented and subsequently exploited. A parametric study is conducted for two limiting cases, where the flange–web joint is assumed to be pinned or rigid. For a chosen set of geometries, the most undesirable parametric spaces are identified for both global and local slendernesses, in terms of the strut length and the flange width respectively, where highly unstable behaviour is observed in the post-buckling range. Practical implications are discussed in terms of the idealized design strength relationship.