The ex vivo expansion of hematopoietic cells is a developing area with emphasis on bioreactor systems for amelioration of culture conditions. A rational design of bioreactors, especially those allowing microgravity, could permit the production of stem cells and will offer new approaches for studying the mechanisms of proliferation, differentiation, and signal transduction of cultured cells. The efficacy of two commercially available bioreactors (rotating-vessel miniPERM and static INTEGRA CL 350) to support long-term bone marrow cell cultures (LTBMCC) and three-dimensional growth of Hodgkin's lymphoma HD-MY-Z cells was investigated. In the miniPERM system, the growth of LTBMCC spheroids (containing 30-40 cells) was obtained. An essentially higher content of hematopoietic precursor cells (colony-forming units-granulocyte macrophage) was registered in the rotating-vessel system. In this bioreactor, a growth of large HD-MY-Z spheroids (containing 100-200 cells) was achieved. The composed mathematical models of the physicomechanical behavior of spheroids enabled the evaluation of the revolution frequency increase schedule. The differential equations took into account all inertial effects caused by the production module rotation movement as well as those caused by the relative movement of the spheroid in the fluid. The models aimed at the optimization of the rotation frequency increase schedule for different types of cells to reduce shear stress, augment productivity, and tolerate the growth of large spheroids. The models were numerically tested using MATLAB-SIMULINK software, and the trajectories of prestained HD-MY-Z spheroids were filmed. The coincidence of the theoretical and experimental trajectories was sufficient.