The effectiveness of the longitudinal members such as deckhouse, superstructure, longitudinal bulkhead etc. contributing to the longitudinal strength of ships have been studied by many investigators. The authors have tried to analyse these problems applying the theoretical plane stress system of an elastic rectangular plate, noticing that a ship is a structure assembling rectangular plates in three-dimension. In this first report, they present the deduction of the theoretical plane stress system in a homogeneous elastic rectangular plate so modified the Okubo's theoretical method as suitably applicable to the analysis. As the examples, the stress distributions in simply loaded stress fields are added.