The suspensions of non-Brownian fibers are of interest for many applications. Although many studies concerning suspensions are available in the literature, most of them concern suspensions of spherical particles. In this paper, global and local rheology of fiber suspensions are explored near the jamming transition. A critical volume fraction is extracted from the experimental data. The value of this critical volume fraction is in agreement with the expected value of the concentration of rigid rods above which the isotropic phase becomes unstable. Moreover, non-reversible effects of the shearing are observed in flow curves because of the non-Brownian behavior of the studied fibers.