Abstract: In this study, a truly mesh-free method is implemented for the elastic analysis of discontinues media. The media is divided into separate parts which are connected to each other by the interface layers. The displacement field in each part is constructed by the radial basis point interpolation method, enriched by the polynomial terms. The final system of equations is derived by the substitution of the displacement field into the weak form of the governing equation. The dependency of the method on the background mesh has been taken care of by stabilized nodal integration. Based on derived equations a computer code is developed and some cases are investigated. The results of analyses show that the nodal integration improves the accuracy of results in comparison with the Gauss method. The stability of proposed method is also guaranteed by the suitable choice for shape parameters and the radius of supports.