Magnetorheological elastomers (MREs) represent a class of soft materials characterized by adjustable mechanical and viscoelastic properties through the application of a magnetic field. These materials consist of composite structures in which magnetizable particles are dispersed within solid elastomer bases, aligning themselves into chain-like structures during the curing phase [1]. In this presentation, we will introduce an analytical formulation to characterize a laminate structure [2] composed of layers of MRE alternated with a passive yet more rigid material, such as an aluminium plate. The constitutive equation of the MRE is derived within the framework of finite strain regimes, where an additional internal variable representing the elastic deformation of the matrix is coupled constitutively with the external magnetic field. Consequently, both the elastic moduli and relaxation times become contingent on the external magnetic field. The response of the laminate structure is investigated under forced oscillations. This structured assembly holds potential for creating semi-active dampers, allowing for the dynamic properties to be finely tuned by manipulating the external magnetic field [3]. The analytical framework presented here lays the foundation for understanding and optimizing the behaviour of MRE-based laminates, offering insights into their application in the development of adaptable and controllable damping systems.