A pendulum is attached to an elastically mounted body in cross flow. The body is excited due to the action of vortex shedding. The stability of the semi-trivial solution (representing the vibration of the body with the non-oscillating pendulum) is investigated. It is proved that a certain interval of the vortex shedding frequency can exist where the semi-trivial solution representing the vertical vibration of the body is unstable. The body vibration is the source of parametric excitation of the pendulum resulting in autoparametric resonance.