Morphing aircraft concepts aim to enhance the aircraft performance over multiple missions by designing time variant wing configurations. The morphing concepts require wing skins that are flexible enough to allow large in-plane stretching and high bending stiffness to resist the aerodynamic loads. In this study, an optimization problem is formed to enhance the in-plane flexibility and bending stiffness of wing skins made of composite laminate. Initially, the optimal fiber and elastomer materials for highly flexible fiber reinforced elastomer laminates are studied using materials available in the literature. The minor Poisson’s ratio of the laminate is almost zero for all the fiber and elastomer combinations. In the next stage, the effects of boundary conditions and aspect ratio on the out-of-plane deflection of the laminate are studied. Finally, an optimization is performed to minimize the in-plane stiffness and maximize the bending stiffness by spatially varying the volume fraction of fibers of a laminate. The optimization results show that the in-plane flexibility and bending stiffness of the laminate with a variable fiber distribution is 30–40% higher than for the uniform fiber distribution.