A new two-dimensional feed-forward functionally expanded neural network (2D FFENN) used to produce surface models in two dimensions is presented. New nonlinear multilevel surface basis functions are proposed for the network's functional expansion. A network optimization technique based on an iterative function selection strategy is also described. Comparative simulation results for surface mappings generated by the 2D FFENN, multilevel 2D FFENN, multilayered perceptron (MLP), and radial basis function (RBF) architectures are presented.