In a previous paper of this series – hereinafter to be referred to as [1] – the author introduced a new method for a large class of boundary value problems connected with the flexure analysis of elastic plates of arbitrary shape where the concept of ‘Lines of Equal Deflection’, i.e. lines which are obtained by intersecting the bent plate by planes parallel to the original plane of the plate, was introduced. The present paper extends this analysis to the buckling analysis of thin elastic plates with various forms of boundary conditions. It is shown that the proposed method appears to be a powerful tool for the investigation of those problems of elastic stability which could not be solved by conventional methods because of the difficulty of the mathematical treatment.