Based on the basic equation of electromagnetic elastic motion and the expression of electromagnetic force,the electromagnetic vibration equation of the rectangular thin plate in transverse magnetic field is obtained. According to a rectangular plate with one side fixed and three other sides simply supported,time variable and space variable are separated by the displacement modal expansion and the method of Galerkin,and the two-degree-of-freedom internal resonance nonlinear vibration differential equations are obtained. By the method of multiple scales,the coupled characteristic equations of the first two order vibration modes are obtained under the case of 1∶3 internal resonance. By an example,the time history response diagrams and phase diagrams of the internal resonance amplitude are got. The effects of internal resonance characteristics with initial value and the thickness for undamped system and also the magnetic field intensity for damping system are discussed respectively. The results show that the system presents obvious nonlinear internal resonance characteristics.