In the recent paper, one of the numerical methods without element, for static analysis of thin plates displacement based on classical plates theory (CPT), has been presented. In this method, the domain of problem solving is shown only by the means of a set of nodes, and there is no need to any mesh scheme or element. One of the kinds of element free methods used here is the Radial Point Interpolation Method (RPIM). In order to access to the governing equations, the Hamilton principle is used in the form of Galerkin weak form. Using interpolating functions, the field variables, namely the displacement, are approximated, and by applying the governing equations, the convergence and the accuracy of the present method are studied. Results of the present method are compared with the results of the exact solution of analytical methods of plates and also with the finite element method (FEM). In addition, the effects of thickness ratio to length, appearance coefficient, and node distribution are discussed.