Inverted Pendulum system is a multivariable, unstable, high order and nonlinear system. The inverted pendulum system has a single-input-multiple-output (SIMO) structure where one single input force has to control both angles of the pendulum and the position of the cart at the same time. So far, many kinds of inverted pendulum were implemented such as inverted pendulum on cart and rotational inverted pendulum. The rotational inverted pendulums are mounted on motor shaft and the pole is maintained in vertical position with restricted angle oscillation by controlling the motor. Modeling and system identification are vital part of control engineering theory. The quest for a model can include a very detailed analysis of the physics of the system. In this project, the dynamic and mathematical modeling of inverted pendulum system should be determined and obtained so that the controller and entire system will work efficiently. Complete dynamical modeling will be developed, analyzed and demonstrate using MA TLAB/SIMULINK as an aided software tool.