In this work static analysis of isotropic rectangular plates with variable thickness are presented using three dimensional electricity theory and for first time using radial point interpolation method. Using this numerical method, the field variables are interpolated just using nodes scattered arbitrarily in the plate domain. As there is no connection between any two nodes, their number can be increased in any area and direction to get more accuracy. It is assumed that, the plate thickness varies linearly in y direction or it has parabolic convex/concave lower surface in the y direction. The horizontal upper surface of the plate is subjected to the transverse uniform load in the z direction. Shape functions in this method have Kroneker delta function property and different boundary conditions can be applied easily using elimination approach. Convergence of results for simply supported isotropic rectangular plates with linearly variable thickness is presented for different thickness ratios and compared with available results. Distributions of the deflections and stresses for the plates with parabolic convex/concave lower surface in the y direction and under different boundary conditions are presented in numerous graphs. It has been showed that this numerical method is so appropriate to analyze such plates and have rapid convergence and high accuracy.