The shock tube is a useful tool for simulating the various compressible flows. In the theory of ideal shock tube flow, it is customarily assumed that the unsteady expansion wave generated by diaphragm rupture is a perfectly centered plane wave. However, such wave is generally not centered. In some experimental applications, the question arises as to how to evaluate or characterize the non-centered waveform. In the present research, the numerical study was carried out in order to investigate the effect of the diaphragm rupture of the shock tube on the characteristics of expansion wave. As a result, the effect of diaphragm rupture process on the flow field in the range close to the diaphragm was clarified, and the results obtained from numerical simulations were compared with the experimental ones.