The basic equations of electro-magneto-thermo-elasticity are very complicated. It is hard to obtain analytical solutions, even if the simplest conditions were considered. The approximate method is an effective method to solve the complicate problems. However, the variational principle is theoretical foundation of finite element method and other approximate methods. According to the corresponding relations between generalized forces and generalized displacements, the basic equations of electro-magneto-thermo-elasticity are multiplied by corresponding virtual quantities, then integrated with volume and area, then algebraically added, and integrated with time, the Hamilton-type variational principles of electro-magneto-thermo-elasto-dynamics are established. They are the theoretical foundation of approximate calculation for multi-physics fields problem of electro-magneto-thermo-elasticity-dynamics.