An unusual type of vibration of flattened spheroidal liquid drops, occurring under certain conditions, is described and illustrated. Appropriate liquids placed on a sufficiently hot horizontal surface float on a film of their own vapor, which vapor insulates the drop so that it evaporates quite slowly, this phenomenon being known as the Leidenfrost effect. It is under these conditions that drops have been found capable of sustaining large amplitude regular radial vibrations whose driving force is probably related to the radial flow of vapor below the drops. The vibrating drops are approximately polygons which may have any of 2, 3, 4,…nsides, seen by the eye as drops with 4, 6, 8…(2n+2) regular lobes around the circumference. Methods of exciting and recording the effect are described.