Aluminium alloys are characterised by numerous benefits, such as ease of fabrication, good strength-to-weight ratio, attractive appearance and high corrosion resistance. On the other hand, aluminium has low Young’s Modulus and as a result, it is susceptible to structural instability phenomena that can subsequently affect the structural integrity. Improved strength and stiffness can be achieved by combining aluminium alloys with concrete. The present work investigates numerically the response of concrete-filled aluminium tubular members under axial compression. In particular, 6082-T6 extruded aluminium alloy rectangular and square hollow sections filled with C30 concrete are examined. Finite element models are developed accounting for geometric and material non-linearities. Upon validation against experimental data, the finite element models are used to conduct a thorough parametric study over a wide range of structural members likely to occur in practice to investigate their structural behaviour under axial compression. The obtained load capacities are discussed and remarks on the structural response and on the buckling behaviour are reported. Design recommendations for the buckling strength of concrete-filled aluminium tubular columns on the basis of the numerical analyses are also made.