Abstract: The paper gives out boundary as well as area integral equations with which critical loadings of arbitrary-shaped thin elastic plates with smooth boundary or with boundaries containing a finite number of corner points under various kinds of boundary conditions can be obtained. Furthermore, by means of programming and calculations for a number of typical examples, especially, for the plates with free-edges, satisfactory results show that the method provided in this paper is applicable to the buckl

Key words: boundary element method, thin plate, buckling, fundamental solution.