Abstract:The meshless methods have a relative simple pretreatment process. The Kriging interpolation procedure is one of the meshless methods. Numerical manifold method can solve both continuous and discontinuous deformation problems in a unified mathematical formulation. The finite cover is the essential technique in this method. Both the finite cover technique and Kriging interpolation method are integrated to develop a Kriging interpolation procedure based on finite covers which take advantages of these two types of numerical methods. The merit of the proposed method is that the shape functions constructed using this method have the properties of Kronecker d-function,which will make the essential boundary conditions be easily implemented. The fundamental theory of this procedure is illustrated and numerical analyses of examples show that the proposed procedure is an effective and simple method for singular and discontinuous problems.