In this work, the effect of four factors including the nanoclay (NC) content, polyamide 6 (PA-6) content, compatibilizer type, and amount, as material variables on barrier properties of different high-density polyethylene (HDPE)/PA-6/clay nanocomposites, was described. Response surface method was used as a tool for experimental design. Different PA-6/clay nanocomposites were prepared by melt mixing of PA-6 at different clay loadings using a corotating twin-screw extruder. Subsequently, different PA-6/NC compounds containing different amounts of clay were melt mixed with HDPE to produce blow-molded containers under fixed processing conditions. In order to model the permeability, a neural network modelling approach in combination with a modified version of differential evolution was employed. The differential evolution modifications included, among others, a local search procedure based on backpropagation. The best models determined had a mean squared error in the testing phase of less than 0.1 and an average relative error lower than 12.2%, the difference between experimental results and predictions being within an acceptable range. This indicates that the methodology used was able to efficiently model the considered process.