This paper is concerned with the development of a two-dimensional feed-forward functionally expanded neural network (2D FFENN) surface modeller. 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. The main purpose of this work is the development of a two-dimensional system, able to produce surface data mappings. The main application area of interest for the proposed system is sea surface modelling and target detection by sea clutter suppression.