Tóm tắt: Meshfree methods have gained more and more attention over the last two decades in analyzing mechanical problems because of their high potentials. In this paper, a meshfree method, Radial Point Interpolation method, is used to solve the two-dimensional normal node-to-node contact problems. Some examples of normal contact and tangential contact are considered. A Matlab program is also written to implement the method. The results are compared with FEM results obtained by software ANSYS because analytical solutions are not available.