1D-numerical analysis of the network algorithm with the orifice equation for the relationship between pressure difference and flowrate has been mostly used to analyse leakage flow at the gap. In this study, a 3D-numerical method applying momentum loss model to the gap region in the computational domain is represented to reflect effectively the effect of leakage flow by determining the proportion of pressure difference to air passage velocity. While the 3D-numerical method is verified through the computation of the two compartments model, the numerical analysis of the stack effect in a building stairway is performed. As the temperature of air outside drops, the pressure in the upper stairway and leakage flowrate through the gap in the door rise. The change of gap area does not have an effect on pressure in the stairway for the analysis conditions.