This paper presents a technique using combined finite element and analytical methods for determining the dynamic responses of structures to moving bodies. In previous work (Comput. Struct., submitted), moving masses were treated as moving loads, ignoring inertia effects. This is not always reasonable and the technique described here allows inertia effects to be included in the analysis. In order to illustrate the methodology, and for validation purposes, the technique is first applied to a clamped–clamped beam subjected to a single mass moving along the beam. Finally, it is applied to the problem that initiated the work: to predict the dynamic response of an experimental mobile gantry crane structure due to the two-dimensional motion of the trolley.