Abstract: Based upon the three dimensional theory of mathematical elastic stability, the stability problem of a plate compressed and sheared in two perpendicular direction is studied by the method of initial functions. The governing differential equations of the symmetric buckling mode and asymmetric buckling mode have been formulated. An example of a simply supported rectangular plate with two-way compression is solved, and two buckling mode is obtained. The result shows that the symmetric buckling mode can not exist in the elastic region, and the asymmetric buckling load is lower than that derived from the classic theory.