The topic of this work is a study of the microbuckling behavior of unidirectional fiber-reinforced composite materials. Some alternative finite element discretizations are compared in order to model the characteristic cell. Transversely isotropic material behavior is taken into account to model some anisotropic fibers. The free surface of the matrix has also influence on the fiber microbuckling. The results are compared qualitatively and quantitatively with analytical solutions and experiments.