Flexible substrates enable new capabilities in applications ranging from electronics to biomedical devices. To provide a new platform for these applications, we investigate a composite material consisting of rigid fiber fabrics impregnated with soft elastomers, offering the ability to create load bearing, yet flexible substrates. We demonstrate an integrated and facile one-step imprint lithographic patterning method on a number of fabrics and resins. Furthermore, the bending and tensile properties were examined to compare the composites to other flexible materials such as PET and cellulose paper. Carbon fiber composites possess a higher tensile modulus than PET while retaining almost an order of magnitude lower bending modulus. Fabric composites can also have anisotropic mechanical properties not observed in homogeneous materials. Finally, we provide a discussion of these anisotropic mechanical responses and their potential use in flexible applications.