A mathematical model of calculating the content of carboxyhaemoglobin in the blood of humans exposed to CO has been proposed. Results of comparing the calculation of carboxyhaemoglobin content with the experimental data of human exposure to constant concentration of CO during quiet breathing have been obtained. Results of numerical experiments for determining carboxyhaemoglobin concentration in case of rapid pulmonary ventilation that is characteristic for fire conditions in a room have been shown. The estimates of intervals of CO influence on the human body have been obtained with the use of the analytic solution of the integral model for calculating thermogasdynamics of fire. Critical fire durations obtained with the use of the proposed model and the traditional approach have been compared. It has been shown that the method of calculating the critical fire duration in terms of CO that exists in the scientific and regulatory literature on fire safety can lead to qualitatively and quantitatively incorrect results. © 2017 International Information Institute.