The dynamic response of long structures (e.g., pavements) subjected to moving loads is generally difficult to simulate using conventional methods like the finite element method in the Lagrangian setting. This is because the entire length of the structure in the path of the moving load would need to be discretized, and in turn would require large meshes. Additionally, if improvement in quality of results through the use of finer mesh sizes is sought, the entire region of the mesh in the load path would require refinement. As a direct result, long simulation run-times can be expected when using conventional methods. To overcome these drawbacks, and improve the efficiency of the finite element simulations, the Arbitrary Lagrangian Eulerian (ALE) approach can be used to simulate pavement structures, provided longitudinal homogeneity is assumed. This contribution uses an extension of the quasi-static ALE framework to the transient domain, enabling the study of the dynamic response of pavement structures subjected to moving loads. In this work, some case studies are considered to highlight the capabilities of this dynamic ALE framework.