A node based radial point interpolation method(NS-RPIM)has recently developed for heat transfer problem and solid mechanic problem.In this method,shape functions for field variable are built based on Gaussian basis functions by point interpolation method(PIM).This kind of shape function possess the Kronecker delta property,hence essential boundary can imposed straightforward.The generalized smooth Galerkin weak form is applied to construct the system equation.The method works well with quadrilateral mesh and it can obtain better results with distortive mesh compared with standard FEM.Several numerical examples are studied the properties of the methods in terms of accuracy,convergence and stability with mesh distortion.