The oscillatory flow in a baffled tube reactor provides a significant enhancement of radial transfer of momentum, heat and mass and a good control of axial back mixing at a wide range of net flow rate. But little has been known about reliable details of the three-dimensional structure of flow field in this kind of flow because most published studies in the area were based on the two-dimensional simulation techniques. This paper implemented a three-dimensional numerical simulation study on the asymmetry of flow pattern in the baffled tube reactor which was observed experimentally. A systematic study by numerical simulation was carried out which covered a range of oscillatory Reynolds number (Reo) from 100 to 5,000 and employed models respectively for laminar and turbulent flows. It was found in the simulation that under symmetric boundary conditions the transition from axially symmetric flow to asymmetric one depended on the numerical technique employed in simulation. With a structured grid frame the transition occurred at Reo much greater than that with an unstructured grid frame, for both laminar and turbulent flows. It is not rational that the onset of the transition changes with the accuracy of numerical technique. Based on the simulation results, it was postulated that the asymmetry appeared in simulations with symmetric boundary conditions might result from the accumulation of calculation errors but the asymmetry observed in experiments might result from the slight asymmetry of geometry which exists inevitably in any experiment apparatus. To explore the influence of the slight asymmetry of geometry, the effect of the eccentricity of baffles and the declination of oscillating boundary were studied by use of the finite volume method with a structured grid and adaptive time steps. The simulation result showed that both the eccentricity of baffles and the declination of oscillating boundary have obvious influence on the asymmetry of flow patterns for laminar and turbulent flow. More details were discussed in the paper.