A three-dimensional solution for a fiber-reinforced circular cylinder is presented for axisymmetric force and displacement boundary conditions. The solution, which can satisfy all the boundary conditions prescribed on the curved and end surfaces of the cylinder, can be used directly in the micromechanical analysis of fiber-reinforced composites to investigate the typical representative volume element (RVE). The element consists of a combined circular cylinder composed of a solid inner circular cylinder of transversely isotropic fiber, a concentric enter circular cylinder of isotropic matrix material, and an interface layer between the fiber and the matrix. The radial and tangential flexural compliances of the interfacial material are considered, and their effects on the stress transfer at the interface are studied parametrically. The numerical results presented show that the material properties of the interfacial layer have significant influences on the stress distribution within the RVE, particularly at the cross sections near the ends of the cylinder, where external loads are applied.