The rectangular plate undergoing overall motions was investigated. The dynamic equations were derived through the Finite Element Method and Lagrange equations. Different from the conventional linear modeling method which employs three Cartesian deformation variables, the present modeling method used two nonCartesian variables along with one Cartesian variable to describe the elastic deformation. Therefore the dynamic stiffness terms was captured. The numerical study demonstrated that the equations of motion presented here are more reliable and accurate than the traditional dynamic equations. Some errors will appear if the assumption modal method is used to describe the deformation of flexible plate undergoing overall motions.