The analysis of structures subjected to consecutive moving loads, such as pavement structures under traffic loads, poses considerable engineering challenges. Traditional Finite Element Method (FEM) simulations become costly and complex when dealing with moving loads due to the need for fine meshing throughout the domain. The Arbitrary Lagrangian Eulerian (ALE) formulation offers an efficient approach by treating the load as fixed relative to the ALE reference configuration while allowing the material to move through a fixed mesh. In this work, a novel method for updating the history variables within the ALE formulation is proposed. Each material point is traced back to its position in the previous time step, and the data from this prior position is used to assess the state of the material point at its current location. Comparative examples with standard FEM simulations are conducted, demonstrating that the proposed method performs successfully.