This paper presents a framework to systematically investigate the high-speed train–track–bridge dynamic interactions, aiming to provide a method for analysing and assessing the running safety and the ride comfort of trains passing through bridges, which are critically important for the design of new high-speed railway bridges. Train–track–bridge interactive mechanism is illustrated. A fundamental model is established for analysing the train–track–bridge dynamic interactions, in which the vehicle subsystem is coupled with the track subsystem through a spatially interacted wheel–rail model; and the track subsystem is coupled with the bridge subsystem by a track–bridge dynamic interaction model. Modelling of each subsystem and each interactive relationship between subsystems are presented. An explicit–implicit integration scheme is adopted to numerically solve the equations of motion of the large non-linear dynamic system in the time domain. Computer simulation software named the train–track–bridge interaction simulation software (TTBSIM) is developed to predict the vertical and lateral dynamic responses of the train–track–bridge coupled system.