Underactuation and nonminimum phase properties of a robotic two-link flexible manipulator (TLFM) have attracted many researchers to use various types of control techniques for its desired outcome. The most focused problem of a two-link flexible manipulator is the trajectory tracking and vibration control. It is seen, in the literature, that some research works have tackled the tracking and vibration control of TLFM in the presence of disturbances added in the position where torque is added. However, in this paper, using a disturbance observer and sliding mode control technique is designed to accomplish the link vibration and joint angle trajectory tracking control of a TLFM in the presence of unmatched disturbances. The unmatched disturbance is estimated with the help of a disturbance observer. The simulation results obtained using MATLAB confirm that the joint angle trajectory tracking and link vibration control of the considered TLFM are achieved successfully and the proposed technique works effectively.