The complexity of the evacuation process is associated with the flow of occupants through various egresses available inside the building. Several methods and algorithms are now available to analyse the problem related to evacuation. In the present paper an algorithm, evacuation discrete time model (EDTM) has been presented to analyse the building egress evacuation time problem with previous works. The algorithm is based on the crowd flow theory and uses discrete computational approach to identify various widths of egresses available for movement of the people, which is more accurate and practicable because the crowd flow rate is variable. The developed model has been compared with an existing model to show the capabilities of the developed algorithm. A case of stadium stand egress is chose for the validity of EDTM, and a comparison of EDTM, previous model and computer simulation indicates that both the EDTM and the simulation curves were found to give better predictions than the previous model. Based upon the comparison analysis with stranded crowd and evacuation crowd at a certain time, EDTM shows great value in explaining the cause of stampede-trampling and crushing incident of egress or narrow passage zone.