Abstract: The localized deformation of matrix plays an important role in determining the failure process of composites. In the current work, based on the finite element analysis, a proper elasto-plastic constitutive model considering the softening after yielding was introduced using the user-defined material mechanical behavior (UMAT) subroutine. Then the evolution of the localized deformation of matrix during the unidirectional tensile test of the fiber/epoxy composites was presented. The effect of the post-yield softening character of the polymer matrix on the loading transfer in the fiber/epoxy composites was studied. The results show that the stress distributions of fiber and the plastic deformation of matrix are nonuniform. The localized deformation of matrix reduces the degree of the stress concentration of the adjacent fiber. The range of the stress concentration in adjacent fiber becomes wider, while the stress concentration degree degrades, with the inter-fiber spacing increasing.