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In modern engineering, micro-heterogeneous materials are designed to satisfy the needs and challenges in a wide field of technical applications. The effective mechanical behavior of these materials is influenced by the inherent microstructure and therein the interaction and individual behavior of the underlying phases. Computational homogenization approaches, such as the FE2 method have been found to be a suitable tool for the consideration of the influences of the microstructure. However, when real microstructures are considered, high computational costs arise from the complex morphology of the microstructure. Statistically similar RVEs (SSRVEs) can be used as an alternative, which are constructed to possess similar statistical properties as the realmicrostructure but are defined by a lower level of complexity. These SSRVEs are obtained from a minimization of differences of statistical measures and mechanical behavior compared with a real microstructure in a staggered optimization scheme, where the inner optimization ensures statistical similarity and the outer optimization problem controls themechanical comparativity of the SSRVE and the real microstructure. The performance of SSRVEs may vary with the utilized statistical measures and the parameterization of the microstructure of the SSRVE.With regard to an efficient construction of SSRVEs, it is necessary to consider statistical measures which can be computed in reasonable time and which provide sufficient information of the real microstructure.Minkowski functionals are analyzed as possible basis for statistical descriptors of microstructures and compared with other well-known statistical measures to investigate the performance. In order to emphasize the general importance of considering microstructural features by more sophisticated measures than basic ones, i.e. volume fraction, an analysis of upper bounds on the error of statistical measures and mechanical response is presented. © Springer International Publishing Switzerland 2015.