Transverse stress concentrations are mainly governed by the polygonal cross section of fibers generating stress concentrations near the corners and the high stiffness mismatch of steel fibers and epoxy matrix. Micro-scale images show that there is a slight radius at the polygon corners instead of sharp corners. First, the effects of these radii on the stress concentrations are investigated. Then, in order to decrease the stress concentrations, the idea of introducing a transition region with nano-reinforcements between fiber and matrix is investigated. Finite element models are generated in micro-scale to investigate these cases in which fibers and matrix are generated separately. The results show that the polygonal cross sections significantly decrease stress concentrations, whereas the variation introduced to the fiber-matrix interface reduces only the normal component of stresses and if the fiber/volume fraction is low.