Abstract. Lateral pedestrian loads and flexible footbridge form a dynamic interaction system, which has a special lock-in phenomenon and results the instability of the dynamic system when the pedestrian number reaches certain critical value. A simplified theoretical equation to model the dynamic interaction system and to estimate critical pedestrian number is proposed. The lateral pedestrian loads resulted by structural vibration is first analyzed from a view point of social force model. And then, combined with structural vibration equation, the control differential equation for describing the dynamic interaction system is proposed. The control equation explains why the lock-in phenomenon is resulted and how to estimate the critical pedestrian number. Two typical footbridges are investigated and the results show that critical pedestrian number estimated by the model is more close to those by field observation.