Abstract: The two-dimensional magnetic-elasticity problem of a current-carrying rectangular plate under the coupled actions of the electromagnetic field and the mechanical field is studied. Based on the nonlinear magneto-elastic kinetic equations, the geometric equations, the physical equations, the electrodynamics equations and the expressions of Lorentz force of thin rectangular plate, the corresponding difference form and linearized iteration equations are developed. And the numerical solutions for these equations are obtained. A rectangular plate with four edges fixed is used as an example to demonstrate the stresses and the deformations under the coupled actions of the electromagnetic field and mechanical load. The magneto-elastic effect on the plate by the side current and electromagnetic induction density is studied. The results show that the states of the deformation, the stress and the strain in thin plate can be controlled by changing relevant parameters of the magnetic field strength, and thus the current density and carrying capacity of thin plate components can be enhanced to accomplish an optimum design of engineering structures.