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A main problem of direct homogenization methods is the high computational cost, when we have to deal with large random microstructures. This leads to a large number of history variables which needs a large amount of memory, and moreover a high computation time. We focus on random microstructures consisting of a continuous matrix phase with a high number of embedded inclusions. In this contribution a method is presented for the construction of statistically similar representative volume elements (SSRVEs) which are characterized by a much less complexity than usual random RVEs in order to obtain an efficient simulation tool. The basic idea of the underlying procedure is to find a simplified SSRVE, whose selected statistical measures under consideration are as close as possible to the ones of the original microstructure. © 2010 Springer Science+Business Media B.V.