A vehicle track model is developed with the objective of providing new capabilities in modelling track vibration response. Understanding track vibration is essential to evaluating the durability of track components and the vibration energy transmitted to the vehicle. A new element model is derived herein that represents a track span as a continuous elastic member with distributed inertia. This model captures the e!ects of static track sag, static track tension, and the coupling of longitudinal and transverse track vibration. Results from a companion experimental study on a section of track are reviewed and support the use of this continuum approximation over a well-de"ned frequency spectrum. The track element model is then extended to describe an entire track circuit for an example military vehicle. An eigenanalysis of this circuit model leads to the system vibration modes that are subsequently employed in a low order model for forced response. The forced response characteristics resulting from two major excitation sources, roadarm motion and polygonal action, are described. The modal content of the track response is then examined to determine the minimum size model required to describe low-frequency track vibration. It is concluded that such low order system models o!er an e$cient alternative to established large degree-of-freedom multi-body track models.