An articulated pipe composed of a flexible pipe and a rigid pipe is a typical hybrid rigid-flexible dynamical system involving flow-induced vibrations. Based on Hamilton′s principle, the governing equations of motion of the hybrid rigid-flexible pipe system were established. The partial differential equations of motion were discretized via Galerkin′s approach using the modal functions of a cantilevered beam. Instabilities and critical flow velocities were analyzed and calculated as a function of the stiffness of the rotational spring, mass ratio, length ratio of the rigid and flexible pipes. The results show that the critical velocities decrease as the increasing of length ratio and the system mainly suffers second mode instability. The hybrid pipe undergoes complicated transference of “second mode instability-regain stability-third mode instability” at a certain value of stiffness when the flow velocity increases. With the increasing of mass ratio of flexible pipe, a transition from second mode instability to fourth mode instability is observed.