Interface between fiber and matrix as a stress transfer medium determines composite performances in load-bearing structures. For instance, failures in composite are most likely initiated by an accumulation of interfacial cracks allowing little or no stress transfer from the matrix to the fiber and vice versa. This paper studies stress transfer behaviors at the interface subject to axial and transverse loadings using the finite element method. Single fiber surrounded by matrix was modeled by introducing a cohesive zone model (CZM) at the interface taking into account the bonding mechanism. By the proposed technique, plastic deformation in the matrix and exerted friction at the interface was verified to govern the role of stress transfer at the interface. Further, the influence of other fibers in matrix surrounding the model was also discussed.