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A computational method is proposed for the construction of statistically similar representative volume elements (SSRVEs) for discontinuous fiber composites (DFCs) in order to enable an efficient calculation of material properties based on computational homogenization. The SSRVEs are obtained by solving an optimization problem which minimizes the difference between the power spectral density of a target microstructure and its simplified one. The SSRVEs are constructed for target microstructures serving as examples for DFCs, which are validated by means of comparing the mechanical properties of the target microstructures with the ones of the SSRVEs. The results show that the mechanical properties of the SSRVEs agree with the target microstructures and that the SSRVEs can extremely reduce the computational costs of finite element analyses to derive macroscopic material properties of DFCs. © 2018 Elsevier Ltd