Expanded polystyrene is used in diverse applications, notably for protective and structural purposes. Its cushioning and mechanical strength excel under compressive loads, especially when optimally designed. A key factor influencing its compressive stress is the initial density, which plays a significant role in determining the material’s mechanical properties. This aspect is primarily determined by the bead size distribution. Although there is a vast body of literature on modeling the stress response of expanded polystyrene, there is limited emphasis on predictions that account for this factor, which is also relevant for the manufacturing of the material. Recent literature has emphasized the capability of artificial neural networks in predicting the compressive behaviors of expanded polystyrene, incorporating various factors. In this study, artificial neural network models were used to predict the compressive stress responses of polystyrene foams, with a focus on bead size distribution parameters. Specimens of two distinct initial densities were examined using micrographs to identify bead diameters and distributions, which were then used as model inputs. Compression tests on these specimens were conducted at two different rates. The collected data facilitated the development of predictive models for the material’s compressive behavior. The model predictions closely match experimental findings, with error metrics showing deviations <3% compared to the experimental data. This highlights the utility of artificial neural networks in modeling the compressive behavior of polystyrene foams, particularly when bead size and related parameters are considered.