The specifics of application of the topological optimization process to the random cellular biomimetic structures created on the basis of morphological composition of the natural materials are considered in this paper. An approach to morphology optimization of representative volumes elements (RVEs) of cellular polymeric 3D printed samples with a random structure depending on loading conditions with respect to specified stiffness requirements has been implented. A problem definition is given for the investigation of the effect of topological optimization on porous cellular structures, with different volume fractions of matrix material. A comparative analysis of the characteristics of finite element models before and after the optimization process was performed.