In composite materials, fiber/fiber interaction and the resulting stress concentration phenomenon due to a fiber failure are crucial in determining the composite fracture behavior. A number of mathematical models have been developed for calculating the stress concentration factor (SCF) and predicting its dependence on the properties of the composite constituents. None of the existing models separately considers the case of tension and compression. This could be due to the force-balance approach used, which assumes the phenomenon to be the same in both cases. In this study, micro-Raman spectroscopy (MRS) was used to investigate the stress concentration phenomenon and measure experimentally the stress concentration factor in graphite/epoxy composites subjected to tensile and compressive stress. The results showed that the stress concentration in tension is different from that in compression. The radius of the zone of influence is much higher when the composite is under compressive stresses. The maximum SCF in both cases, however, was 1.5 ± 0.05, limited by the ability of the interface to transfer shear stresses. The difference in stress concentration is attributed primarily to the difference in the interfacial behavior of the composite under tension and compression. The results are discussed and explained from both fracture mechanics and energy viewpoints.