This paper presents a dynamic model of a single-link flexible link-flexible joint manipulator system. The Lagrange method and the assumed mode method are combined in the modeling process, and multiple factors affecting the motion of the flexible manipulator system are considered, such as the coupling effect of link flexibility and joint flexibility, gravity, input torque, and the influence of the mass and inertia of the load and rotor on the system. Subsequently, the derived model is numerically simulated by MATLAB using the fourth-order Runge–Kutta method.