Development of cell-mediated scaffold technologies for the treatment of critical bone defects is very important for the purpose of reparative bone regeneration. Today the properties of the bioreactor for cell-seeded scaffold cultivation are the subject of intensive research. We used the mathematical modeling of rotational reactor and construct computational algorithm with the help of ANSYS software package to develop this new procedure. The solution obtained with the help of the constructed computational algorithm is in good agreement with the analytical solution of Couette for the task of two coaxial cylinders. The series of flow computations for different rotation frequencies (1, 0.75, 0.5, 0.33, 1.125 Hz) was performed for the laminar flow regime approximation with the help of computational algorithm. It was found that Taylor vortices appear in the annular gap between the cylinders in a simulated bioreactor. It was obtained that shear stress in the range of interest (0.002-0.1 Pa) arise on outer surface of inner cylinder when it rotates with the frequency not exceeding 0.8 Hz. So the constructed mathematical model and the created computational algorithm for calculating the flow parameters allow predicting the shear stress and pressure values depending on the rotation frequency and geometric parameters, as well as optimizing the operating mode of the bioreactor.