Morphing aircraft wings require flexible skins that can undergo large strains, have low in-plane stiffness and very high out-of-plane flexural bending stiffness. The large strain capability is especially important for gross morphing applications such as span change where the skins may be required to undergo axial strains of the order of 50% or greater. Low in-plane stiffness allows morphing to be accomplished at a reasonable energy cost while high bending stiffness ensures that skin sections between supports do not suffer from significant out-of-plane deformation under aerodynamic pressure loads. For some morphing applications (for example, wing span-, chord-, or camber-change), the required deformation is mostly one-dimensional. In such a case, a Flexible Matrix Composite (FMC) skin is proposed as a possible solution. A FMC comprises of stiff fibers (for example fiberglass) embedded in a soft high-strain capable matrix material (for example, silicone). The idea is to align the matrix-dominated direction along the morphing direction. This allows the skin to undergo large strain at low energy cost. However, the high-stiffness in the fiber-dominated direction, along with applied tension along the fiber-dominated direction is critical in providing the membrane skin with a large out-of-plane stiffness and consequently, the ability to withstand aerodynamic pressure loads. An analysis for a FMC skin panel under in-plane axial loads and out-of-plane pressure loads is developed, and this is validated against experiment. The analysis is then used to conduct design studies. A comparison of the FMC skin to a skin comprising of just the matrix material illustrates the importance of the fiber's stiffness in resisting out-of-plane deformation under pressure loading. The influence of the matrix and fiber properties and applied tension on the out-of-plane deformations and morphing capability is examined in detail.