Unwanted vibrations caused by the commanded motions lower the positioning accuracy and degrade the control performance of flexible link manipulators. Much work has been devoted to the dynamics and control of flexible link manipulators. However, there are few studies dedicated to the flexible link manipulators having Duffing oscillator dynamics. This paper develops a new model for a flexible single-link manipulator by assuming large mechanical impedance in the drives or large inertia of the motor hub and by considering the flexibility of the single-link manipulator. The derived model includes an infinite number of uncoupled Duffing oscillators by ignoring the modal coupling effects. Two new methods are presented for controlling the vibrations of the flexible manipulator governed by Duffing oscillators. One is designed for the single-mode Duffing oscillator, and the other is for the multi-mode Duffing oscillators. A comparison of these two methods is made using the results of numerical simulations and experimental measurements. Experimental investigations are also performed on a flexible single-link manipulator to validate the dynamic behavior of Duffing oscillators and the effectiveness of the new control methods.