A homogenization technique applied in conjunction with limit analysis theory allows the prediction of the macroscopic strength of fiber composites as a function of the strength properties of the phases (i.e. fiber, matrix and interface). Emphasis is placed here on the uniaxial strength, for which bounds based on static and kinematic approaches are proposed. Special attention is devoted to the influence of the matrix, which is presumed to be polymeric and complying with Drucker-Prager, Mohr-Coulomb or a parabolic type criterion. Also the limited strength of the fiber-matrix interface is accounted for through the introduction of a Mohr-Coulomb type strength criterion. Analytical equations describing the dependence of the macroscopic strength of the composite on the orientation of the applied stress with respect to the fibers are proposed. The parameters required to define the model are limited in number and possess a clear mechanical meaning. Comparisons with experimental data available in the literature prove quite satisfactory.