The behavior of the long rectangular plate, fixed at each ends and subjected to a uniform hydrostatic pressure, is studied in this paper. Elastic and plastic strains are considered, and the relation of strains and stresses are assumed as a Fig. 1. From the theoretical calculation, the following conclusions may be drawn, 1. The relation of pressure and deflection almost agrees with the work made by Young. 2. The ranges of plastic zone and the extreme fiber strains at fixed ends are obtained.