The mechanical behavior of polymer–matrix composites uniaxially reinforced with carbon or glass fibers subjected to compression/tension perpendicular to the fibers was studied using computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure idealized as a random dispersion of parallel fibers embedded in the polymeric matrix. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces, and the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Composites with either perfect or weak fiber/matrix interfaces (the latter introduced through cohesive elements) were studied to assess the influence of interface strength on the composite behavior. It was found that the composite properties under transverse compression/tension were mainly controlled by interface strength and the matrix yield strength in uniaxial compression/tension.