The poor formability of Mg results in crack and failure in workpiece material during rolling process and limits its applications in different industries. Numerical modeling of the process can guarantee that the required product properties are met with a minimum production cost. The numerical modeling of the rolling processes requires the coupling of several models including different physical phenomena such as the deformation of the workpiece with its thermo-metallurgical evolution and the thermal evolution of the rolls with its mechanical deformation. On the other hand, in finite element modeling of the rolling process, the meshes of the workpiece are often highly distorted. The high distortion in meshes decreases the confidence in the predicted results. Many formulations based on the viscoelasticity behavior of workpiece material are encountered in the literature to model the rolling process, each with their pros and cons. This present work introduces the Coupled Eulerian-Lagrangian (CEL) formulation, in which the workpiece is divided into three regions (unrolled, in rolling deformation, rolled) to simulate material flow during the process. The comparison of the results with the literature shows that the temperature and strain fields are well predicted by the proposed model. All of the simulations have been done in the two-dimensional mode with ABAQUS/Explicit software.