The inverted pendulum pedestrian model (IPM) for walking on laterally-oscillating structures, originally proposed by Macdonald, has been recently calibrated based on data from pedestrians walking on a laterally-oscillating instrumented treadmill. It was then generalised to be suitable for the application in a predictive manner, i.e. in simulations of lateral structural response for any population of pedestrians. The generalised IPM captures the fundamental pedestrian-structure interaction mechanism and pedestrian-generated lateral forces onto a structure, including the self-excited forces which are critical from the point of view of structural stability. However, since the closed-form solutions of the generalised IPM are currently unavailable, its application requires numerical integration. To address this shortcoming, closed form solutions for the long-term average lateral self-excited forces are derived in this study based on the framework introduced by McRobie. A parametric study is conducted revealing complex interdependencies between pedestrian and bridge behaviour and their influence on the self-excited forces. The presented results are related to the measurements from full-scale bridges and laboratory investigations. •Analytical solutions are derived for the calibrated and generalised IPM.•Phase drift and synchronisation are considered for pedestrian stepping behaviour.•Analytical solutions are verified against results obtained from numerical simulations.•A parametric study is conducted to understand the dependence of self-excited forces.•Results are compared with measurements from laboratories and full-scale bridges.