One of the main challenges for fiber-reinforced polymers (FRP) is the difficulty to predict their mechanical behavior. At the microscale, the properties of the constituents, their spatial distribution and the defects arising from manufacturing affect the mechanical behavior. In this work, statistically representative volume elements (SRVEs) are proposed based on a micromechanical finite element model to determine the effect of content, distribution and size of microstructural defects and, material uncertainties on the elastic mesoscale properties of FRPs. To that end, different cylindrical void sizes are considered as well as irregular shaped voids between fiber tows (inter-fiber voids). Fibers and voids are randomly distributed in a SRVE. An uncertainty quantification and management analysis is employed to obtain statistical descriptors of the effective mesoscale mechanical properties of FRPs. The results obtained are compared with analytical models. It is demonstrated that, for carbon fiber/epoxy composites, SRVEs with lateral dimensions equivalent to 15 times the average fiber diameter and a length of 0.01 mm along the longitudinal direction remain statistically representative with or without the presence of voids. The results show that the presence of voids reduces the transverse and shear elastic properties of FRPs. The smaller the voids are, the bigger is the reduction. Regarding the presence of inter-fiber voids, the reduction is lower. This trend is well predicted by the Mori–Tanaka mean field theory. However, the relative difference between the numerical and the analytical predictions increases for high void volume fractions. Regarding the effective longitudinal Young's modulus, the rule of mixtures, the Mori–Tanaka mean field theory and the concentric cylinder assembly model provide similar predictions for the mean value, but the uncertainty is overestimated by the analytical models because the properties of the fibers take a single value for each calculation with the analytical model, while they more realistically change from fiber to fiber in the numerical SRVEs.