The aim of the present work is to passively reduce the induced drag of the rear wing of a Formula One car at high velocity through aeroelastic tailoring. The angle-of-attack of the rear wing is fixed and is determined by the required downforce needed to get around a turn. As a result, at higher velocity, the amount of downforce and related induced drag increases. The maximum speed on a straight part is thus reduced due to the increase in induced drag. A fibre reinforced composite torsion box with extension-shear coupled upper and lower skins is used leading to bending-torsion coupling. Three-dimensional static aeroelastic analysis is performed loosely coupling the Finite Element code Nastran and the Computational Fluid Dynamics panel code VSAERO using ModelCenter. A wing representative of Formula One rear wings is optimised for minimum induced drag using a response surface methodology. Results indicate that a substantial induced drag reduction is achievable while maintaining the desired downforce during low speed turns.