Abstract Thin-walled steel hollow sections are used extensively in the construction, offshore, mining and security industries. Such members subjected to blast loads are of interest due to increased security demands and the occurrence of accidental or intentional explosive events. This paper reports an experimental and analytical investigation of steel square hollow sections subjected to transverse blast load, applied with explosive uniformly distributed along the length of the member. Three different section sizes were tested over three different lengths, and the members were fully clamped at their ends. The explosive loads were sufficient in magnitude to cause plastic deformation of the cross-section (local deformation), plastic flexural deformation of the overall member (global deformation), and tensile tearing at the supports. The energy dissipated in the local deformation is determined using rigid-plastic analysis and yield line mechanisms of the deformed cross-sections. The total input energy minus the energy dissipated in local deformation is assumed to be expended in flexural deformation. Analytical solutions using the energy consumed in flexural deformation are shown to produce bounded solutions of the transverse plastic deformation of the members. Finally, a semi-empirical solution is suggested that can be used to aid in design.