Concrete-filled　round-ended　elliptical　hollow　section　(CFREHS)　columns　are　gradually　coming　into　use　as　piers　and　arches　in　engineering　practice,　owing　to　their　unique　properties　concerning　aesthetic　perception　and　low　flow　resistance　coefficients.　However,　there　has　been　a　paucity　of　studies　focusing　on　the　structural　behaviour　and　design　methods　for　CFREHS　columns.　The　present　study　has　involved　investigating　the　behaviour　of　eccentrically-loaded　CFREHS　stub　columns.　A　nonlinear　numerical　model　that　adopts　an　equivalent　stress-strain　model　for　the　novel　type　of　confined　core　concrete　was　established,　and　verified　via　experimental　data.　Subsequently,　the　effects　of　various　parameters　on　the　eccentric　compressive　response　of　CFREHS　stub　columns　were　analysed,　including　the　diameter-to-thickness　ratio,　load　eccentricity　ratio,　and　the　cross-section　slenderness.　Eccentric　compressive　capacities,　failure　patterns,　strength　indexes,　stress–strain　responses,　contact　stress,　typical　force-displacement　curves,　and　M–N　curves　of　eccentrically　pressured　CFREHS　stub　columns　were　also　evaluated.　The　findings　of　the　numerical　analysis　indicated　that　the　eccentric　load　bearing　capacity　of　CFREHS　stub　columns　evidently　increased　for　increases　in　the　cross-section　area,　steel　strength,　and　concrete　strength,　while　the　opposite　was　observed　for　increases　in　the　load　eccentricity　ratio　and　diameter-to-thickness　ratio.　Finally,　simplified　empirical　formulae　were　presented　to　predict　the　eccentric　load　bearing　capacities　of　CFREHS　stub　columns.　The　results　of　the　study　are　expected　to　provide　a　reliable　reference　for　application　to　the　proposed　CFREHS　columns　in　concrete-filled　steel　tube　(CFST)　structures.　©　2018　Elsevier　Ltd