To make clear the nature of hull vibration of higher mode it is indispensable to investigate the problem of the coupling of hull vibration and local vibration of ships. This problem was investigated already by Prof. Watanabe, Dr. Suetsugu and others in connection with the causes of the stern vibration of ships. In these investigations, however, they analysed the problem by replacing the structure which makes a local vibration with a system of spring and mass. As a first step to investigate this problem more closely, in this paper we have analysed the same problem by treating the bottom structure, the typical structure which makes a local vibration, as an elastic plate instead of replacing it with a system of spring and mass. After this investigation the nature of so-called second spectrum owing to the coupling of hull vibration and bottom vibration of ships have been made clear. We think that the interesting phenomena found in the experiments of box beams and sometimes in the tests on actual ships are closely connected with the two nodes or three nodes vibartion of second spectrum explained in this paper.