Both the finite-cover technique and radial point-interpolation method are integrated together to develop an element-free radial point-interpolation procedure based on finite covers which takes both advantages of these two types of numerical methods. The shape functions constructed by the proposed method have the property of Kronecker ? -function which made 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 with higher computational accuracy.