The stress fields in the components of a unidirectional composite due to shrinkage and external loads are computed for 20 matrix/reinforcement combinations having various volumetric contents. Further, the load transmissions between loaded and unloaded fibers are formulated as three- dimensional elasticity solutions. The instability problem of a composite is treated by both the static and the energy method, resulting in critical loads and buckling wavelengths which depend on material constants and geometries. The theoretical results are in good agreement with experiments. The work reported herein encompasses the following principal areas: (1) parametric studies (internal stresses and displacements computed for unidirectional composites comprised of different matrices and reinforcements combinations and different volumetric contents); (2) three-dimensional load transfer among loaded and unloaded fibers in a matrix; (3) buckling of fibers in a matrix under axial load as an elasticity solution; (4) the buckling of fibers in a matrix under axial load, solved with the Ritz-Galerkin method; and (5) buckling of fibers in a matrix due to matrix shrinkage.