Recent advances in manufacturing of multifunctional materials have provided opportunities to develop structures that possess superior mechanical properties with other concurrent capabilities such as sensing, self-healing, electromagnetic and heat functionality. The idea is to fabricate components that can integrate multiple capabilities in order to develop lighter and more efficient structures. In this regard, due to their combined structural and electrical functionalities, electrically conductive carbon fiber reinforced polymer (CFRP) matrix composites have been used in a wide variety of applications in most of which they are exposed to unwanted impact-like mechanical loads. Experimental data have suggested that the application of an electromagnetic field at the moment of the impact can significantly reduce the damage in CFRP composites. However, the observations still need to be investigated carefully for practical applications. Furthermore, as the nature of the interactions between the electro-magneto-thermo-mechanical fields is very complicated, no analytical solutions can be found in the literature for the problem. In the present thesis, the effects of coupling between the electromagnetic and mechanical fields in electrically conductive anisotropic composite plates are studied. In particular, carbon fiber polymer matrix (CFRP) composites subjected to an impact-like mechanical load, pulsed electric current, and immersed in the magnetic field of constant magnitude are considered. The analysis is based on simultaneous solving of the system of nonlinear partial differential equations, including equations of motion and Maxwell's equations. Physics-based hypotheses for electro-magneto-mechanical coupling in transversely isotropic composite plates and dimension reduction solution procedures for the nonlinear system of the governing equations have been used to reduce the three-dimensional system to a two-dimensional (2D) form. A numerical solution procedure for the resulting 2D nonlinear mixed system of hyperbolic and parabolic partial differential equations has been developed, which consists of a sequential application of time and spatial integrations and quasilinearization. Extensive computational analysis of the response of the CFRP composite plates subjected to concurrent applications of different electromagnetic and mechanical loads has been conducted. The results of this work verify the results of the previous experimental studies on the subject and yield some suggestions for the characteristics of the electromagnetic load to create an optimum impact response of the composite.