Consider two coaxial round circles with the same radius. A mathematical model of a tiny liquid drop trapped between them are constant mean curvature (CMC) surfaces because a CMC surface is a critical point of the area for all variations that preserve the enclosed volume and satisfy given boundary condition. A CMC surface is said to be stable if the second variation of the area for any such variation is nonnegative. In this paper, we judge the stability of one period of the so-called unduloid between two consecutive bulges rigorously for the first time.