The cart-and-pendulum system is a highly nonlinear and under-actuated system that is a great source of interest and motivation for researchers all over the world. There are various configurations of the cart-and-pendulum system that finds wide applications in areas of manufacturing, robotics and control. This paper presents an offline mode control of the Flexible Inverted Pendulum (FIP), which is an extended version of conventional rigid-link pendulum system. The flexibility induced in the pole gives an additional degree of freedom to the system. The nonlinear differential equations were derived using Newton's second law of motion. The study inculcates Fuzzy-based Adaptive Neuro Fuzzy Inference System (ANFIS) controllers for achieving the desired objective. The performance of controllers was measured and compared in a Matlab-Simulink environment. The study considered the effect of friction during motion of the proposed system. The results clearly showed that the ANFIS controller effectively mimics and optimises the behaviour of the Fuzzy controller. The number of Fuzzy rules were also significantly reduced using the ANFIS techniques.