This paper illustrates the steps necessary to model the dynamics of a model rubber-tyred gantry (RTG) crane as used in container-handling operations. Various modelling criteria are discussed with the emphasis placed on the importance of non-linear coupling between the chosen system coordinates. The machine is treated as three rigid bodies, these being the gantry itself, the trolley (which is constrained to lateral motion across the top beam) and the spreader. Tyre deformations and structural deflections are not considered in this work. The paper culminates in three non-linear ordinary differential equations, which are then solved numerically for a variety of different cases. An important feature of this work is that the dynamic simulations include complicated gantry motions, not currently designed for, such as combined translations and simultaneous rotations. Such motions are more commonly encountered in mobile robots. However, RTG design needs to move in this general direction in the future if significant and potential performance gains are actually to be realized in practise. The paper concludes with suggestions for implementation of the dynamic model within a fuzzy logic control system.