The article deals with mathematical modelling of flows of people on the basis of a modified stochastic individual-flow approach which represents the flow as a collective movement of individuals, each of whom situationally reacts to changes in the external environment. These changes may involve approaching individuals, emerging obstacles to be avoided, reduced visibility, the psychological conditions of a person, etc. The combination of these factors conditions a trajectory of the person’s movement in the flow, his or her speed while continuing on this trajectory and all this is modelled on the basis of the finite automata theory by way of the object-oriented programming. The motion of the flow is modelled by shifting the elliptical projections of individuals during a small discrete amount of time. Taking into account the possibility of verification of such shifts and depending on the totality of variable conditions it describes the situation occurring during a given time interval. Modelled is the confluence of flows of different densities. The proposed methodology enables one to determine the time in which the flows of people pass through the building including the one under construction taking into consideration the changing situation in the course of the motion. This may be used when preparing design solutions, for planning plots of land within urban territories, to time evacuations from buildings, and when designing communication premises in them.