Fiber-reinforced composites are the most widely used composite materials. For instance, fiber-reinforced polymers are extensively used in aerospace applications where materials with low density but high strength and stiffness are required. Fiber-reinforced composites can be classified into two broad groups: continuous-fiber composites and discontinuous- or short-fiber composites. A unidirectional fiber composite in which all the fibers are aligned in one direction is transversely isotropic so long as the fibers are positioned uniformly or randomly in space. The elastic properties of a fiber-reinforced composite are determined from the analysis of an individual concentric cylinder composed of isotropic linearly elastic fiber and matrix phases. The analysis of the response of a single concentric cylinder to a given applied strain allows the determination of four of the five independent elastic constants of a transversely isotropic composite. Randomly oriented short-fiber composites are macroscopically isotropic and can be modeled as laminated systems.