Elliptical hollow sections (EHS) have been recently added to the family of hollow steel sections available to the construction industry. Their merits include different flexural rigidities about the two principal axes offering efficient bending resistance about the major axis and an aesthetically pleasant appearance. A number of recent practical applications have emerged, which are outlined in this thesis. Previous research on elliptical hollow sections has mainly focused on the cross-section level with a set of design rules for cross-section classification and shear resistance being proposed. The current study reviews the existing cross-section classification limits for both circular and elliptical tubular sections and investigates member instability of EHS in bending (lateral torsional buckling) and under combined axial compression and bending. Reliability analyses to establish a set of reliable design rules for elliptical hollow sections in the Eurocodes and other international structural design codes have been also performed. The key components of this research include laboratory testing, numerical modelling, and development of statistically verified design guidance. A series of experimental studies were undertaken to investigate the buckling response of elliptical hollow section members in bending and under combined axial load and bending. In total, 8 beams, 6 columns and 27 beam-columns were tested; the test results were then used to calibrate finite element models. Parametric studies were performed utilizing the validated numerical models. Based on the experimental and numerical findings, reliability analyses were undertaken to verify design rules for elliptical hollow sections. It is envisaged that these design rules will be incorporated into future revisions of Eurocode 3.