A numerical model simulating the behaviour of elliptical concrete-filled columns under either concentric or eccentric compressive load has been developed in ABAQUS. The numerical results have been compared against a range of experimental results for ultimate load, load–deflection behaviour and failure modes, with good agreement observed. An extensive parametric study has been undertaken whereby the slenderness, load eccentricity, cross-sectional geometry and reinforcement ratio of the concrete-filled columns were varied, creating a data set upon which to formulate design guidance since currently there are no specific provisions in the European Standard EN 1994-1-1 [1] for the design of concrete-filled steel elliptical section columns or beam-columns. It is shown that the current provisions of EN 1994-1-1 [1] for the design of concrete-filled steel columns of circular or rectangular cross-section are also appropriate for the design of members of elliptical cross-section, employing either buckling curve b or c, depending on the level of steel reinforcement. Finally, an assessment is made of the reliability of the design proposals for concrete-filled elliptical hollow section columns and beam-columns.