Morphing structures that are both light-weight and remain conformal to the airfoil are promising candidates for the next generation of aircraft high-lift systems. Notably, variable stiffness materials have also been studied for the application in morphing structures for their potential to enhance structural performance. In this study, a design optimization has been conducted for a morphing trailing edge using a honeycomb core of axial variable stiffness. Utilizing variable stiffness materials in morphing trailing edge leads to a possible reduction in the actuation energy requirement and also enables geometric control of the deformed morphing trailing edge, resulting in enhanced aerodynamic and aeroacoustic performance of the airfoil. Firstly, effects of geometric changes in the deformed morphing trailing edge on the aerodynamic performance of airfoils are characterised through wind tunnel tests. A design optimization is then carried out to inversely identify the honeycomb core axial stiffness parameters which match the target trailing edge deformation shape. In the optimization scheme, a layer-wise sandwich beam model is developed to predict the structural behaviour of the flap with the material stiffness variation considered. Twodimensional fluid/structure static aeroelastic interaction analysis coupling the beam model to an aerodynamic routine is performed in the design optimization using chosen material properties. Optimization results indicate that variable stiffness material provides performance improvement for morphing structures and the present model can be used in the preliminary design of morphing trailing edge devices using variable stiffness materials.