In the investigation of ship's local vibration, the equilibrium equation is to be got under consideration of rectangular plate, not only with stiffeners but also with various appendics. Among those appendices, it is assumed, masses on the rectangular plate, or elastic pillars can be sufficient factors. In this paper, the author is dealing with the conditions of rectangular plate with these appendices. As regarding the studying of these problems, Mr. Kanazawa presented “On the Lateral Vibration of Square Plate with any distributed Load”, or “A problem about ship's Local Vibration” in which he deduced the solutions through integral equation. The author for more various boundary conditions, deduced the solutions through the matrix equation. These both methods are two points of view for seizure of physical phnomenon, and it is reasonable that the both are to coincide consquently. But in the easiness of numerical calculation, it is probable that great difference can be between the both methods.