In this paper, Instability of plates with a circular hole supported at all edges and subjected to shearing forces and/or compressive forces, is studied to investigate the buckling strength of girder web of large ships. The body of this paper consists of two parts ; one is the case where the I-Beam is supported at both ends and is loaded by a concentrated load at the center, so that web of I-Beam is subjected to simple shear and buckled mainly due to the shearing stress. (Fig. 1 and 2) Another is the case where the square plate with a circular hole is subjected to edge thrust under the supported condition along all edges, and the effect of position of the circular hole is mainly studied. (Fig. 11) The buckling loads are determined by Δ²-method and are calculated by Energy method. The conclusions obtained are as follows ; (1) It is proved theoretically and experimentally that Δ²-method (the linear relationship between load P and the square of the max deflection δ²) is also valid for the case of shear buckling (Fig. 4, and 5) (2) The behavior of I-Beam with hole in web and the effect of the hole on the shear buckling strength of the web, are clarified. (Figs. 8, 9 and 10) (3) The effect of position of a hole on the buckling strength of square plate is studied, and the hole is shifted to the transverse direction (4 A) is found to be the weakest. (Fig. 13) (4) It is proposed that to calculate the buckling load of the practical problems such as the buckling strength of a plate with a hole of irregular shape, a numerical distribution of stresses should firstly be computed by a suitable method, for example, finite element analysis, and a suitable deformed mode of the plate should be assumed so as to satisfy the given boundary conditions, then the energy method could easily give the solution with enough accuracy.