Using the multi-phase flow simulation facility described in the software CFX 4.1 and by incorporating bubble breakup and bubble coalescence models, a numerical method was developed and applied to estimate the local gas holdup distribution within bubble columns and aerated stirred vessels under various operating conditions. The calculated local gas holdup values were integrated into the overall gas holdup of the system. The accuracy of the overall gas holdup value under a certain condition was verified by comparing it with an experimental value, which was the liquid height difference before and after aeration obtained by means of visual observation. To assure the applicability of this numerical approach to the gas-liquid flow system, transient gas-liquid flow patterns in bubble columns were also calculated and compared with the snapshots of Delnoij et al. (1997). It is found that both the local and overall gas holdup values show fairly good agreement with the experimental ones if the gas within the aerated stirred vessel is dispersed effectively (N-A<0.03) and the bubble column is operated in the homogeneous regime. The results obtained in this study indicate that the proposed numerical approach can be used to reliably predict gas and liquid flows in stirred vessels and bubble columns.