The plastic collapse response of structural steel elliptical hollow section (EHS) profiles in compression is examined in this paper. As an initial step, a parametric study to identify the factors that determine which plastic mechanisms would arise has been carried out using finite element (FE) results from the current work and experimental data from the literature. All investigated EHS had a cross-sectional aspect ratio of two. The parametric study revealed four plastic collapse mechanisms and showed that the “split flip disc” plastic collapse mechanism is the most likely to appear in compressed EHS. Thus, the present work is focussed on this failure mechanism, for which an analytical model to describe the relationship between load and deformation is developed. Coupled with the consideration of the elastic, yielding and strain hardening characteristics of steel, the derived analytical model enables construction of the full load–deformation behaviour of compressed EHS to be established. The parameters controlling the shape and size of the plastic hinges have been investigated and found to be of key importance; hence, special care has been taken in their definition. Finally, the developed load–displacement curves have been compared with both finite element results and experimental data. The comparisons have revealed good agreement, confirming the ability of the analytical model to predict the collapse response of elliptical tubes.