In this first report the vibration of the engine room of the ship is theoretically analysed. In other reports 11), 12), 13) the author has studied effects of many decks, deck openings and pillars to the vibration of the main structure of the transverse section, which is constructed with members of bottom, the lowest deck and both side frames, by ignoring the correlation of longitudinal members. In this paper the vibratory behavior of the engine room in the three dimensional state is studied by taking in correlational effects of longitudinal members to the transverse members. Eigenvalue equations of the engine room in the symmetrical and asymmtrical modes of the vibration of both transverse and longitudinal sections are acquired.