Current advanced engineering composites suffer from high-cost of manufacturing as well as design and processing weaknesses. On the other hand, nature produces high-performance composites under benign conditions using simple constituents. Hence, it seems that imitating nature constitutes the future of material science. This thesis attempts to answer some of the basic questions concerning the formation of biological fibrous composites. Microstructural studies of these materials have revealed that they exhibit a common architecture known as twisted plywood. This architecture results from the passage of the matrix into a cholesteric liquid crystalline phase during the development of the composite. The main objectives of this work are: to develop a mathematical model based on the well-established liquid crystalline theory of Landau-de Gennes, to describe the formation process of the twisted plywood architecture; to solve the set of governing partial differential equations, to use the theoretical and computational results obtained to provide a picture of the structure evolution and its kinetics.