This paper will present a numerical method for solving fully coupled dynamic problems of the mechanical behavior of electrically conductive composite plates in the presence of an electromagnetic field. The mechanical behavior of electrically conductive materials in the presence of an electromagnetic field is described by the system of nonlinear partial differential equations (PDEs), including equations of motion and Maxwell's equations that are coupled through the Lorentz ponderomotive force. In the case of thin plates, the system of governing equations is reduced to the two-dimensional (2D) time-dependent nonlinear mixed system of hyperbolic and parabolic PDEs. This paper discusses a numerical solution method for this system, which consists of a sequential application of the Newmark finite difference time integration scheme, spatial (with respect to one coordinate) integration scheme, method of lines (MOL), quasilinearization, and a finite difference spatial integration of the obtained twopoint boundary-value problem. The final solution is obtained by the application of the superposition method followed by orthonormalization.