Abrasive flow machining (AFM) is an economic and effective non-traditional machining technique, which is capable of providing excellent surface finish on difficult to approach regions on a wide range of components. With this method, it has become possible to substitute various time-consuming deburring and polishing operations that had often lead to non-reproducible results. In this paper, group method of data handling (GMDH)-type neural networks and Genetic algorithms (GAs) are first used for modelling of the effects of number of cycles and abrasive concentration on both material removal and surface finish, using some experimentally obtained training and testing data for brass and aluminum. Using such polynomial neural network models obtained, multi-objective GAs (non-dominated sorting genetic algorithm, NSGA-II) with a new diversity preserving mechanism are then used for Pareto-based optimization of AFM considering two conflicting objectives such as material removal and surface finish. It is shown that some interesting and important relationships as useful optimal design principles involved in the performance of AFM can be discovered by the Pareto-based multi-objective optimization of the obtained polynomial models. Such important optimal principles would not have been obtained without the use of both GMDH-type neural network modelling and multi-objective Pareto optimization approach.