The developed mathematical model was applied for study of fluid dynamics in a rotational bioreactor for bone tissue engineering by in vitro technology. The research goal is finding an optimal mode for rotation ensuring proper cyclic loading from fluid upon the cell-seeded biomaterial. The basis for developing a mathematical model of a bioreactor was a design of rotational type biological reactor used in medical research; the liquid flow is generated through viscosity mechanism due to surface rotation. Mathematical description of flow in a reactor cavity was performed with Navier—Stokes equations. It was assumed that flow regime in the boundary layer is laminar. Numerical algorithm was accomplished using a fluid flow solver “Fluent” in the code package ANSYS-12. Four variants of generating the rotational motion in the reactor cavity were considered. A series of parametric computations was performed for the rotation frequency f in the range 0.05 ≤ f ≤ 0.25 Hz. The paper offers visualization of velocity fields in the vertical plane. The distributions for shear stress and pressure in the working zone of reactor were calculated and analyzed. Simulations demonstrated that a method of fluid rotation by driving the outer cylinder with an offset axis is the best for arranging a cyclic pressure and cyclic shear stress on the biological material.