This paper presents a study of the flow-induced vibration of an elliptical cross section at various angles of attack immersed in a free stream. The body is elastically-mounted and constrained to move only in the cross-stream direction. Two-dimensional direct numerical simulations are used to study the system response as a function of the spring stiffness and the angle of attack. The elliptical cross section used has an aspect ratio Γ = 1.5. This aspect ratio is large enough so that the deformation from a circular cylinder is obvious, but not so large that the geometry is not related to the cylinder. Because of this, the impact of the symmetry of the system on the flow-induced vibration is studied without also introducing other complexities such as sharp corners or fixed separation points. The body is light with a mass ratio (body mass to displaced fluid mass) of one. The results show a surprisingly wide range of different flow regimes. For small angles (where the body is slightly streamlined) the flow behaviour is similar to that of a cylinder. However, for large angles, where the body is far from symmetric with respect to the wake centreline, the flow can be markedly different with distinct asymmetric modes, including one which is period-doubled. For angles where the body regains its symmetry (aligned across the flow and slightly bluff), an asymmetric mode continues to exist, apparently the result of a spontaneous symmetry breaking that is dependent on Reynolds number. Large- amplitude oscillations persist for very low stiffness or high reduced velocity, and this is explained in terms of the dependence of a critical mass on the angle of attack.