The use of stack may enhance natural ventilation and contaminates migration of buildings. Previous studies have presented some models for quantification of stack effect, however, rarely paid attention to interaction between the shaft and its adjacent space, particularly when there is warmer (or lighter) currents expelled from the adjacent space into the shaft. A quantitative model is developed in this paper for convection of a shaft, both with warm gas expelling from its adjacent space and connected to a cold exterior through top and bottom openings. The model can predict the vertical distributions of temperature and pressure, mass inflow rate, neutral plane location, and is extended to determine the conditions for transition from unidirectional to bi-directional convection. Good agreements are obtained between the predictions of the analytical model and a more sophisticated model, Large Eddy Simulation. To identify the most influential parameters and to quantify their effects on the stack effect, sensitivity studies are conducted with respect to both the shaft configuration parameters (opening area, cross-sectional area and height) and the properties of expelling gas (temperature and mass flow rate). In addition, the critical conditions for transition from unidirectional to bi-directional flow are shown for a hypothetical shaft. (c) 2013 Elsevier B.V. All rights reserved.