A new methodology, namely, artificial neural network (ANN) approach was proposed for modeling and predicting flow behavior of the polyethylene melt through nanochannels of nanoporous alumina templates. Wetting length of the nanochannels was determined to be a function of time, temperature, diameter of nanochannels, and surface properties of the inner wall of the nanochannels. An ANN was designed to forecast the relationship between the length of wetting as output parameter and other aforementioned parameters as input variables. It was demonstrated that the ANN method is capable of modeling this phenomenon with high accuracy. The designed ANN was then employed to obtain the wetting length of the nanochannels for those cases, which were not reported by the wetting experiments. The results were then analyzed statistically to identify the effect of each independent variable, namely, time, temperature, diameter of nanochannels, and surface properties of the inner wall of nanochannels as well as their combinations on the wetting length of the nanochannels. Interesting results were attained and discussed.