AbstractIn this article, a meshless barycentric interpolation collocation method (BICM) with coordinate transformation is proposed to solve the governing partial differential equations (PDEs) for bending, free vibration and buckling problems of irregular plates. First, the coordinate transformation equations for first to fourth derivatives are introduced. Then the PDEs and boundary conditions defined in a physical domain are transformed into a rectangular domain (reference domain) with the derived differential interpolation matrices. The presented BICM can solve the PDEs based on the reference domain and is adaptive to irregular problem domains. Finally, the bending, free vibration and buckling problems of Kirchhoff plates with irregular shapes are studied with the proposed method. To illustrate the effectiveness of the proposed method, the results are compared with those given by theoretical solutions, finite element methods and literature.