In this paper, finite element based modelling and observer based backstepping control of 2-DOF Serial Flexible Link Manipulator (2DSFLM) is presented. The Dynamics of Flexible link manipulators (FLMs) possess mechanical flexibilities in the links, unlike rigid manipulator. Precise dynamic models that can describe the flexibility with the rigid dynamics are required, to design an effective control strategy for these manipulators. This paper exhibits a finite element method (FEM) for the dynamic modelling of 2DSLFM. Tip tracking control of 2DSLFM is difficult because of the non-minimum phase bahaviour. To minimize this difficulty novel control algorithm is proposed. The proposed novel controller is a combination of the state observer and backstepping control. This composite controller offers a way of applying the robust control to each subsystem. Dynamic modelling and control of 2DSFLM are developed and simulated in MATLAB and SIMULINK environment to investigate the performance of the framework. The controller converges the output position and speed to its desired trajectories, and the better transient response is achieved.