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Despite considerable interest among engineers and scientists, bi-directional interaction between walking pedestrians and lively bridges has still not been well understood. In an attempt to bridge this gap a biomechanically inspired model of the human response to lateral bridge motion is presented and explored. The simple inverted pendulum model captures the key features of pedestrian lateral balance and the resulting forces on the structure. The forces include self-excited components that can be effectively modelled as frequency-dependent added damping and mass to the structure. The results of numerical simulations are in reasonable agreement with recent experimental measurements of humans walking on a laterally oscillating treadmill, and in very good agreement with measurements on full-scale bridges. In contrast to many other models of lateral pedestrian loading, synchronisation with the bridge motion is not involved. A parametric study of the model is conducted, revealing that as pedestrians slow down as a crowd becomes more dense, their resulting lower pacing rates generate larger self-excited forces. For typical pedestrian parameters, the potential to generate negative damping arises for any lateral bridge vibration frequency above 0.43 Hz, depending on the walking frequency. Stability boundaries of the combined pedestrian–structure system are presented in terms of the structural damping ratio and pedestrian-to-bridge mass ratio, revealing complex relations between damping demand and bridge and pedestrian frequencies, due to the added mass effect. Finally it is demonstrated that the model can produce simultaneous self-excited forces on multiple structural modes, and a realistic full simulation of a large number of pedestrians, walking randomly and interacting with a bridge, produces structural behaviour in very good agreement with site observations.