Abstract: A submarine pipeline under laying operation forms a long slender rod having the shape of a plane curve according to the effect of the gravity. The lower part lies on the sea bottom and the upper end is supported by a vessel. The vibration of the vessel induced by sea waves generates forced vibration of the pipeline in the vertical plane, and possibly gives rise to dynamic instability and generates parametric vibration off the plane. These vibrations are regarded as small motions about the large static deflection, and the instability regions and the response in these regions are studiod in this paper via the motion equations established. Approximate analytical methods are used in the solution so that the effects of the tension and the geometry of the static deflection curve on the vibrations and the stability can be expressed explicitly.