In this work, we extend Hamilton’s principle in a continuum mechanic framework by the electromagnetic quantities to provide a systematic approach to material modeling. This approach has the significant advantage of ensuring thermodynamic consistency. At least since Albert Einstein’s famous work about moving matter, we know that electrodynamics can only be fully described in a relativistic context. For this reason, we reduce our system to the well-known quasi-static electric and magnetic limits as proposed by Woodson and Melcher. Our approach begins by applying Maupertuis’s principle and integrating the linear momentum along its path. This gives us a Hamilton functional for the matter part. To include the interaction with the charges themselves, we repeat this procedure for the charges. As in the work of Landau and Lifshitz, we have to use not the linear momentum of the charges, but rather the generalized linear momentum. While their work allows only the description of charges in free space, our approach enables the derivation of both mechanical and electromagnetic quantities through the summation of both components. Specifically, this includes electric quantities in the electric limit and magnetic quantities in the magnetic limit, using Hamilton’s principle of stationary action.