Elliptical hollow sections (EHS) represent the recent addition to the range of tubular structural products. Their distinct closed nature brings structural efficiency by offering differing flexible rigidities about each of the principal axes as well as high torsional stiffness. It also offers an interesting and unusual smooth streamlined appearance which can be utilised to fulfil contemporary streamlined appearance which can be utilised to fulfil contemporary design visions. The varying radius of curvature around the circumference characterises the distinctive structural behaviour of EHS from other tubular sections. In this study, the manifestation of local buckling under compression and in-plane bending about each of the principal axes has been examined, and a system of cross-section classification has been proposed.