One of the main difficulties in the development of meshless methods using the Moving Least Squares approximation, such as Mixed Discrete Least SquaresMeshless (MDLSM) method, is the imposition of the essential boundary conditions. In this paper the RPIM shape function, which satisfies the properties of the Kronecker delta condition, is employed in the Mixed Discrete Least SquaresMeshless (MDLSM)method for solving the elasticity problems. Accordingly, two new MDLSM formulation is proposed in this article namely RPIM-based MDLSM and coupled MLS-RPIM MDLSM formulation. The essential boundary conditions can be imposed directly in both presented methods.The proposed methods are used for the solution of three benchmark elasticity problems and the results are presented and compared with the available analytical solutions and those of MLS-based MDLSM formulation. In addition, in each example different types of nodal distributions, regular and irregular configurations, are considered to test the performance of the presented methods. The numerical tests indicates higher accuracy of the suggested approaches in comparison with the MLS-based MDLSM method.