In this study, 3D Representative Volume Element (RVE) models are used to investigate the effect of fiber waviness not only on the Young's moduli but also on the shear moduli and Poisson's ratios of unidirectional discontinuous fiber reinforced (DFR) composites. In order to measure the sole influence of fiber waviness, properties of the RVE model with curved fibers are compared with those of the RVE model with corresponding straight fibers. This comparison shows that fiber waviness significantly affects E11 and moderately affects all the other effective properties. Variation in E22 due to fiber waviness is contrary to general expectations. It is observed that E22 initially decreases and then increases with the increase in fiber waviness. Influence of fiber volume fraction (Vf), fiber/matrix material property mismatch, fiber spatial distribution and fiber/matrix interphase region on the effective properties of DFR composite with curved fibers is also numerically investigated. It is found that Vf, material property mismatch and interphase region have strong influence whereas spatial distribution has weak influence on the effective properties of unidirectional DFR composite containing curved fibers. © 2014 Elsevier B.V. All rights reserved.