Complex mechanical response of fiber-reinforced composite materials presents rich possibilities for enhancing their structural properties by subjecting them to additional electromagnetic, thermal, chemical, etc. treatment. In particular, existing experimental evidence suggests that exposure of a composite material to the electromagnetic field leads to changes in the material's strength and resistance to delamination. These phenomena may be associated with changes in composite material properties caused by an electromagnetic field, and/or changes in the stress state of the composite structural component due to coupling of the mechanical and electromagnetic fields. In the present paper we focus our attention on the macroscopic coupling mechanism and derive a coupled nonlinear system of 2D equations of motion and Maxwell's equation that account for the mechanical and electrical anisotropies of composite orthotropic plates. Within the described framework we study the mechanical response of transversally isotropic graphite/epoxy composite plates in the presence of electromagnetic loading. Interacting effects of mechanical and electromagnetic fields are investigated.