In the field of direct homogenization methods large representative volume elements (RVE's) cause a high computational cost, which is indicated by a large number of history variables allocating a large amount of memory. Additionally, a high computation time is necessary to solve the systems of equations on the micro-scale as well as on the macro-scale. In this contribution we focus on random microstructures consisting of a continuous matrix phase with a high number of embedded inclusions with arbitrary morphology. We present a method for the construction of statistically similar representative volume elements (SSRVE's) which are characterized by a much less complexity than usual RVE's in order to obtain an efficient simulation tool. The basic goal of the underlying procedure is to find a SSRVE, where some selected statistical measures describing the inclusion morphology are as close as possible to the ones of the original arbitrary microstructure.