This paper is concerned with the development of a two-dimensional feed-forward functionally expanded neural network (2D FFENN) surface modeler. New nonlinear 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, Multi-layered Perceptron (MLP) and Radial Basis Function (RBF) architectures are presented.