To obtain date for establishing new methods of estimating critical frequencies of the various modes of vertical flexural vibration of a ship's hull, and at the same time to investigate the predominent factors affecting the vibration of a ship, the author carried out a series of vibration tests on board four cargo vessels of the three-island type under construction or just before completion, using an oscillation exciter which he has newly designed and illustrated in the previous paper. In this paper he reports the results of these experiments from which not only new approximate formulae are established for estimating the critical frequencies of the vertical vibration of a ship's hull in the course of initial design, but also the following problems are partly made clear. (1) The effect of the position of exciting unbalanced force on the vibration of a ship's hull. (2) The damping factors of the flexural vibration of a vessel. (3) The fore-and-aft horizontal vibration induced by the vertical one.