Applying the general method of solution developed in the first paper of this study, buckling problems of elastic plates are treated extensively in this paper. To reduce the labour of numerical calculations, the double integrations of various energy terms are transformed into the simpler line integrals by means of Gauss' Theorem and application of these formulae are generally proved very effective in energy approach of plate problems by several examples, especially in the case of polygonal plates. Using the stress distribution determined by the finite element method, the buckling problem of a perforated square plate under uniaxial compression is studied by the method of numerical calculalion.