Dynamic modeling and controller design for a flexible four-bar mechanism is studied. The fully coupled nonlinear equations of motion are obtained through a constrained Lagrangian approach. Resulting differential-algebraic equations are solved numerically to obtain the system response. A linearized dynamic model is developed which facilitates design of various controllers. The fully coupled nature of the governing equations facilitates control of elastic motion through the input link alone. A simple PD and a robust μ-synthesis controller are shown to be efficient in suppressing the vibrations of the flexible link as well as controlling the rigid body motion.