A variational model that describes the nonlinear interaction between global and local buckling of an imperfect thin-walled I-section strut under pure compression is developed. An initial out-of-straightness of the entire strut and an initial local out-of-plane displacement in the flanges are introduced as a global and a local type of imperfection respectively. A system of differential and integral equilibrium equations is derived for the structural component from variational principles, an approach that was previously validated. Imperfection sensitivity studies focus on cases where the global and local critical loads are similar. Numerical results reveal that the strut exhibiting cellular buckling (or ‘snaking’) is highly sensitive to both types of imperfections. The worst forms of local imperfection are identified in terms of the initial wavelength, amplitude and degree of localization and these change with the generic imperfection size and highlight the potential dangers of unsafe predictions of actual load-carrying capacity.