Expanded polystyrene foams are widely used materials for various applications in engineering, including their use for protective designs. For this type of application, in engineering analysis and design, it is required to know the mechanical response to compression of this type of material, since energy parameters that support the analysis of the effectiveness of a design are derived from it. One of these parameters is strain hysteresis, through which it is possible to know how capable a material is of absorbing energy. The modeling and prediction of this parameter is a challenge from the analysis point of view. This contribution presents a method based on feed-forward artificial neural network models that address a modeling approach to derive this parameter from the mechanical response of expanded polystyrene foam. From this, models are constructed that can predict the response of such material to various density and loading rate conditions. The best of a total of 30 neural network models, which are capable of deriving energy parameters such as hysteresis, is chosen. The results show that this approach is valid for the deformation energy analysis of expanded polystyrene foams since results consistent with the material phenomenology and errors of less than 3% with respect to experimental data are obtained.