The present article deals with a continuum mechanics-based method to model an electro-magneto-rheological (EMR) fluid deformation under an electromagnetic field. The proposed method follows the fundamental laws of physics, including the principles of thermodynamics. We start with the general balance laws for mass, linear momentum, angular momentum, energy, and the second law of thermodynamics in the form of Clausius-Duhem inequality with Maxwell’s equations. Then, we derive the generalized constitutive relation for EMR fluids following the representation theorem. To validate of the same, the developed constitutive relation is applied to an electro-rheological fluid valve system. The analytical predictions of the considered system are consistent with the experimentation. At last, we simulate different velocity profiles from the developed constitutive relation in the case of the parallel plate configuration. As a result, we succeed in providing more physics-based analytical findings than the existing studies in the literature.