Abstract: In this paper, a quadrilateral plate bending element with shear deformations is used for the buckling analysis of thin and moderately thick plates, which satisfies the "Individual Element Test" and is based on the "Free Formulation". The stability parameters of the square plates which are under uniaxial and hiaxial compressions are computed. The difference between conforming and nonconforming geometric stiffness is studied preliminarily. Satisfying numerical resultsare given. And the further discussion for the buckling problem of moderately thick plate is also significant.