Inverted pendulums are traditional dynamic problems. If an inverted pendulum is used in a moving cart, a new type of exciting issues will appear. One of these problems is two-wheeled inverted pendulum systems. Because of their small size, high performance in quick driving, and their stability with controller, researchers and engineers are interested in them. In this paper, a new configuration of one specific robot is modeled, and its dynamic behavior is analyzed. The proposed model can move in two directions, and with a proper controller can keep its stability during the operation. In this robot, two cantilever beams are on the two-wheeled base, and they are excited by voltages to the attached piezoelectric actuators. The mathematical model of this system is obtained using the extended Hamilton’s Principle. The results show that the governing equations of motion are highly nonlinear and contain several coupled partial differential equations (PDEs). In order to extract the natural modes of the beams, the undamped, unforced equations of motion and boundary conditions of the beams are used. If a limited number of modes (N1 and N2) are selected for each beam, the coupled PDEs will be changed to N1 + N2 + 5 ordinary differential equations (ODEs). These complex equations are solved numerically, and the natural frequencies of the system are extracted. The system is then simulated in both lateral and horizontal plane movements. The simulation shows that the governing equations are correct, and the system is ready for designing a proper controller. It should be mentioned that in the future works, the derived equations will be validated experimentally, and a suitable control strategy will be applied to the system to make it automated and more applicable.