This paper provides an insight into ongoing research aimed at designing a morphing wing with the ability to continuously adapt its aerodynamic shape. The wing is targeted at a general purpose unmanned aerial vehicle. The morphing wing concept outlined in the paper is based on continuous camber changes of the wing leading and trailing edges, allowing optimal performance in different flight regimes. The aeroelastic tailoring method is used to design the load carrying structure of the wing in order to define the optimal stiffness and strength of the structure, which are considered as fixed in subsequent design steps. The research proposes a novel modular design approach that combines aerodynamic shape optimisation and aeroelastic considerations for designing morphing wing surfaces.