Closed-cell polymer foams are versatile materials that have multiple applications in several industries due to their mechanical energy absorption capabilities, and they are used to design protective devices as engineering solutions or to produce packaging solutions to protect goods. Because most of these products and devices operate in compression, it is necessary to know the material behavior to compressive loadings for modeling and design purposes. In this work, the compressive response of a closed-cell expanded polypropylene polymer foam is modeled using feed-forward artificial neural network models as a case study. Practical considerations and a methodology that includes the basic steps to conduct the modeling of the compressive stress of foams of this class are presented. The modeling uses foam densities, loading rates, and strain as inputs in an artificial neural network system to model compressive stress in the foam. Results help conclude that feed-forward neural networks can model the response at compression for expanded polypropylene foams considering different variables since prediction errors close to the unity of the coefficient of determination R2 and error results below 2% regarding testing data were obtained.