In general, a deck plate of a box girder such as ship hull is subjected to inplane tensile and/or compressive load due to longitudinal bending. A deck plate is a main strength member of a box girder, and is stiffened by stiffeners and girders in the longitudinal and transverse directions to prevent overall buckling under compressive load. When the strength of a deck plate is considered, the plate elements subdivided by stiffeners and girders play an important role, and the precise evaluation of their compressive strength is necessary. In this paper, as a series of research, the compressive ultimate strength of a rectangular plate is theoretically investigated as follows. (1) The mode of initial deflection is measured on 33 deck panels of Bulk Carrier and Pure Car Carrier, and the coefficients of components of initial deflection are calculated. (2) A series of elastic-plastic large deflection analysis is performed assuming the measured mode of initial deflection. According to the results of calculation, it is due to the effect of large deflection that inplane rigidity reduces in the middle part of the plate in the case of thin plate, while it is due to the local plastification by bending in the case of thick plate. (3) Based on the results of calculation, deflection method and curveture method are proposed to predict the compressive ultimate strength of thin plate and thick plate, respectively. In both methods, a rectangular plate with uni-modal initial deflection is considered which is equivalent in behavior to the actual panel. It is demonstrated that these methods predict the compressive ultimate strengths which have good relations with calculated ones. (4) Effective coefficient of initial deflection is more precisely evaluated, and its simple formula is proposed.